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Wiese KJ. Theory and experiments for disordered elastic manifolds, depinning, avalanches, and sandpiles. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:086502. [PMID: 35943081 DOI: 10.1088/1361-6633/ac4648] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2021] [Accepted: 12/23/2021] [Indexed: 06/15/2023]
Abstract
Domain walls in magnets, vortex lattices in superconductors, contact lines at depinning, and many other systems can be modeled as an elastic system subject to quenched disorder. The ensuing field theory possesses a well-controlled perturbative expansion around its upper critical dimension. Contrary to standard field theory, the renormalization group (RG) flow involves a function, the disorder correlator Δ(w), and is therefore termed the functional RG. Δ(w) is a physical observable, the auto-correlation function of the center of mass of the elastic manifold. In this review, we give a pedagogical introduction into its phenomenology and techniques. This allows us to treat both equilibrium (statics), and depinning (dynamics). Building on these techniques, avalanche observables are accessible: distributions of size, duration, and velocity, as well as the spatial and temporal shape. Various equivalences between disordered elastic manifolds, and sandpile models exist: an elastic string driven at a point and the Oslo model; disordered elastic manifolds and Manna sandpiles; charge density waves and Abelian sandpiles or loop-erased random walks. Each of the mappings between these systems requires specific techniques, which we develop, including modeling of discrete stochastic systems via coarse-grained stochastic equations of motion, super-symmetry techniques, and cellular automata. Stronger than quadratic nearest-neighbor interactions lead to directed percolation, and non-linear surface growth with additional Kardar-Parisi-Zhang (KPZ) terms. On the other hand, KPZ without disorder can be mapped back to disordered elastic manifolds, either on the directed polymer for its steady state, or a single particle for its decay. Other topics covered are the relation between functional RG and replica symmetry breaking, and random-field magnets. Emphasis is given to numerical and experimental tests of the theory.
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Affiliation(s)
- Kay Jörg Wiese
- Laboratoire de physique, Département de physique de l'ENS, École normale supérieure, UPMC Univ. Paris 06, CNRS, PSL Research University, 75005 Paris, France
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De Polsi G, Hernández-Chifflet G, Wschebor N. Precision calculation of universal amplitude ratios in O(N) universality classes: Derivative expansion results at order O(∂^{4}). Phys Rev E 2021; 104:064101. [PMID: 35030839 DOI: 10.1103/physreve.104.064101] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2021] [Accepted: 11/11/2021] [Indexed: 06/14/2023]
Abstract
In the last few years the derivative expansion of the nonperturbative renormalization group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of its convergence properties allowed for an estimate of the error bars as well as the precise computation of many critical quantities. In this work we extend previous studies to the computation of several universal amplitude ratios for the critical regime of O(N) models using the derivative expansion of the nonperturbative renormalization group at order O(∂^{4}) for three-dimensional systems.
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Affiliation(s)
- Gonzalo De Polsi
- Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay
- Instituto de Física, Facultad de Ingeniería, Universidad de la República, J. H. y Reissig 565, 11300 Montevideo, Uruguay
| | - Guzmán Hernández-Chifflet
- Instituto de Física, Facultad de Ingeniería, Universidad de la República, J. H. y Reissig 565, 11300 Montevideo, Uruguay
| | - Nicolás Wschebor
- Instituto de Física, Facultad de Ingeniería, Universidad de la República, J. H. y Reissig 565, 11300 Montevideo, Uruguay
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Santos-Filho JB, Plascak JA. Monte Carlo simulations of the XY vectorial Blume-Emery-Griffiths model in multilayer films for ^{3}He-^{4}He mixtures. Phys Rev E 2018; 96:032141. [PMID: 29347044 DOI: 10.1103/physreve.96.032141] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Indexed: 11/07/2022]
Abstract
The XY vectorial generalization of the Blume-Emery-Griffiths (XY-VBEG) model, which is suitable to be applied to the study of ^{3}He-^{4}He mixtures, is treated on thin films structure and its thermodynamical properties are analyzed as a function of the film thickness. We employ extensive and up-to-date Monte Carlo simulations consisting of hybrid algorithms combining lattice-gas moves, Metropolis, Wolff, and super-relaxation procedures to overcome the critical slowing down and correlations among different spin configurations of the system. We also make use of single histogram techniques to get the behavior of the thermodynamical quantities close to the corresponding transition temperatures. Thin films of the XY-VBEG model present a quite rich phase diagram with Berezinskii-Kosterlitz-Thouless (BKT) transitions, BKT endpoints, and isolated critical points. As one varies the impurity concentrations along the layers, and in the limit of infinite film thickness, there is a coalescence of the BKT transition endpoint and the isolated critical point into a single, unique tricritical point. In addition, when mimicking the behavior of thin films of ^{3}He-^{4}He mixtures, one obtains that the concentration of ^{3}He atoms decreases from the outer layers to the inner layers of the film, meaning that the superfluid particles tend to locate in the bulk of the system.
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Affiliation(s)
- J B Santos-Filho
- Instituto Federal de Ciências e Tecnologia de Sergipe 49100-000 São Cristóvão, Sergipe, Brazil
| | - J A Plascak
- Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza-Campus I, Departamento de Física-CCEN Cidade Universitária 58051-970-João Pessoa, Paraíba-Brazil.,Departamento de Física-ICEx, Universidade Federal de Minas Gerais Caixa Postal 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.,Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
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Lecoutre C, Guillaument R, Marre S, Garrabos Y, Beysens D, Hahn I. Weightless experiments to probe universality of fluid critical behavior. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:060101. [PMID: 26172640 DOI: 10.1103/physreve.91.060101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2015] [Indexed: 06/04/2023]
Abstract
Near the critical point of fluids, critical opalescence results in light attenuation, or turbidity increase, that can be used to probe the universality of critical behavior. Turbidity measurements in SF6 under weightlessness conditions on board the International Space Station are performed to appraise such behavior in terms of both temperature and density distances from the critical point. Data are obtained in a temperature range, far (1 K) from and extremely close (a few μK) to the phase transition, unattainable from previous experiments on Earth. Data are analyzed with renormalization-group matching classical-to-critical crossover models of the universal equation of state. It results that the data in the unexplored region, which is a minute deviant from the critical density value, still show adverse effects for testing the true asymptotic nature of the critical point phenomena.
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Affiliation(s)
- C Lecoutre
- CNRS, ICMCB, ESEME, UPR 9048, F-33600 Pessac, France
- Université Bordeaux, ICMCB, UPR 9048, F-33600 Pessac, France
| | - R Guillaument
- CNRS, ICMCB, ESEME, UPR 9048, F-33600 Pessac, France
- Université Bordeaux, ICMCB, UPR 9048, F-33600 Pessac, France
| | - S Marre
- CNRS, ICMCB, ESEME, UPR 9048, F-33600 Pessac, France
- Université Bordeaux, ICMCB, UPR 9048, F-33600 Pessac, France
| | - Y Garrabos
- CNRS, ICMCB, ESEME, UPR 9048, F-33600 Pessac, France
- Université Bordeaux, ICMCB, UPR 9048, F-33600 Pessac, France
| | - D Beysens
- Physique et Mécanique des Milieux Hétérogènes, UMR 7636 CNRS - ESPCI - Université Pierre et Marie Curie - Université Paris Diderot, 10 rue Vauquelin, 75005 Paris, France
- Service des Basses Températures, CEA-Grenoble & Université Joseph Fourier, F-38000 Grenoble, France
| | - I Hahn
- Jet Propulsion Laboratory, California Institute of Technology, California 91109, USA
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Dantchev D, Rudnick J, Barmatz M. Finite-size effects in presence of gravity: the behavior of the susceptibility in 3He and 4He films near the liquid-vapor critical point. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 80:031119. [PMID: 19905074 DOI: 10.1103/physreve.80.031119] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2009] [Indexed: 05/28/2023]
Abstract
We study critical-point finite-size effects on the behavior of susceptibility of a film placed in the Earth's gravitational field. The fluid-fluid and substrate-fluid interactions are characterized by van der Waals type power-law tails, and the boundary conditions are consistent with bounding surfaces that strongly prefer the liquid phase of the system. Specific predictions are made with respect to the behavior of 3He and 4He films in the vicinity of their respective liquid-gas critical points. We find that for all film thicknesses of current experimental interest the combination of van der Waals interactions and gravity leads to substantial deviations from the behavior predicted by models in which all interatomic forces are very short ranged and gravity is absent. In the case of a completely short-ranged system exact mean-field analytical expressions are derived, within the continuum approach, for the behavior of both the local and the total susceptibilities.
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Affiliation(s)
- Daniel Dantchev
- Institute of Mechanics, BAS, Academic Georgy Bonchev St building 4, 1113 Sofia, Bulgaria
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Donner T, Ritter S, Bourdel T, Ottl A, Köhl M, Esslinger T. Critical Behavior of a Trapped Interacting Bose Gas. Science 2007; 315:1556-8. [PMID: 17363669 DOI: 10.1126/science.1138807] [Citation(s) in RCA: 140] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Abstract
The phase transition of Bose-Einstein condensation was studied in the critical regime, where fluctuations extend far beyond the length scale of thermal de Broglie waves. We used matter-wave interference to measure the correlation length of these critical fluctuations as a function of temperature. Observations of the diverging behavior of the correlation length above the critical temperature enabled us to determine the critical exponent of the correlation length for a trapped, weakly interacting Bose gas to be nu = 0.67 +/- 0.13. This measurement has direct implications for the understanding of second-order phase transitions.
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Affiliation(s)
- T Donner
- Institute of Quantum Electronics, Eidgenössische Technische Hochschule (ETH) Zürich, CH-8093 Zürich, Switzerland
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Ganshin A, Scheidemantel S, Garcia R, Chan MHW. Critical Casimir force in 4He films: confirmation of finite-size scaling. PHYSICAL REVIEW LETTERS 2006; 97:075301. [PMID: 17026241 DOI: 10.1103/physrevlett.97.075301] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2006] [Indexed: 05/12/2023]
Abstract
We present new capacitance measurements of critical Casimir force-induced thinning of 4He films near the superfluid transition, focused on the region below Tlambda where the effect is the greatest. 4He films of 238, 285, and 340 A thickness are adsorbed on atomically smooth, N-doped silicon substrates. The Casimir force scaling function theta, deduced from the thinning of these three films, collapses onto a single universal curve, attaining a minimum theta=-1.30+/-0.03 at x=td1/nu=-9.7+/-0.8 A1/nu. The collapse confirms the finite-size scaling origin of the dip in the film thickness. Separately, we also confirm the presence down to 2.13 K of the Goldstone or surface fluctuation force, which makes the superfluid film approximately 2 A thinner than the normal film.
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Affiliation(s)
- A Ganshin
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
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9
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Kimball MO, Gasparini FM. Universality and finite-size scaling of the specific heat of 3He-4He mixtures. PHYSICAL REVIEW LETTERS 2005; 95:165701. [PMID: 16241816 DOI: 10.1103/physrevlett.95.165701] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2005] [Revised: 05/27/2005] [Indexed: 05/05/2023]
Abstract
We have measured the heat capacity of (3)He-(4)He mixtures confined in films of thickness 48.3 and 986.9 nm. The confinement is defined by direct bonding of two silicon wafers. The heat capacity is measured using an ac technique and then transformed to correct for exponent renormalization effects. The data address the expected universal critical behavior along the lambda line as function of (3)He concentration. We discuss the results of several analyses of the data, and we show that a universal collapse can be achieved for all the mixtures. However, this is on a locus which differs from that of the pure system. An alternative analysis is also presented which yields collapse of all the data under certain assumptions. We believe these data are the first to test universality of finite-size scaling for the specific heat along a locus of transitions.
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Affiliation(s)
- Mark O Kimball
- University at Buffalo, The State University of New York, 14260-1500, USA
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10
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Scaling predictions for thermodynamical properties of finite-size liquid systems. J Mol Liq 2005. [DOI: 10.1016/j.molliq.2004.07.050] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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11
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Kleinert H, Yukalov VI. Self-similar variational perturbation theory for critical exponents. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:026131. [PMID: 15783402 DOI: 10.1103/physreve.71.026131] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/09/2004] [Indexed: 05/24/2023]
Abstract
We extend field theoretic variational perturbation theory by self-similar approximation theory, which greatly accelerates convergence. This is illustrated by recalculating the critical exponents of O (N) -symmetric phi(4) theory. From only three-loop perturbation expansions in 4-epsilon dimensions, we obtain analytic results for the exponents, which are close to those derived recently from ordinary field-theoretic variational perturbational theory to seventh order. In particular, the specific-heat exponent is found to be in good agreement with best-measured exponent alpha approximately -0.0127 of the specific-heat peak in superfluid helium, found in a satellite experiment. In addition, our analytic expressions reproduce also the exactly known large- N behavior of the exponents.
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Affiliation(s)
- H Kleinert
- Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany.
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12
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Kimball MO, Mooney KP, Gasparini FM. Three-dimensional critical behavior with 2D, 1D, and 0D dimensionality crossover: surface and edge specific heats. PHYSICAL REVIEW LETTERS 2004; 92:115301. [PMID: 15089144 DOI: 10.1103/physrevlett.92.115301] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2003] [Indexed: 05/24/2023]
Abstract
The critical behavior at a second order phase transition is characterized by the divergence of the correlation length xi. We have studied the superfluid transition of 4He in a series of experimental cells in which this divergence of xi is modified due to finite-size confinement. In particular, the design of these cells is such that the smallest dimension is kept the same, 1 microm, but the geometry is such that one obtains crossover to dimensionality of 2, 1, and 0. This corresponds to films, channels, and boxes filled with helium. We measure the specific heat and compare these results with theoretical expectations. We identify surface and line specific heat contributions by analyzing the deviation of the specific heat from its behavior in the thermodynamic limit. The design of these cells is made possible by a combination of silicon lithography and direct wafer bonding.
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Affiliation(s)
- M O Kimball
- Department of Physics, University at Buffalo, The State University of New York, Buffalo, New York 14260, USA
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Vásquez C, Paredes R, Hasmy A, Jullien R. New universality class for the three-dimensional XY model with correlated impurities: application to 4He in aerogels. PHYSICAL REVIEW LETTERS 2003; 90:170602. [PMID: 12786062 DOI: 10.1103/physrevlett.90.170602] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2001] [Revised: 03/07/2003] [Indexed: 05/24/2023]
Abstract
Encouraged by experiments on 4He in aerogels, we confine planar spins in the pores of simulated aerogels (diffusion limited cluster-cluster aggregation) in order to study the effect of quenched disorder on the critical behavior of the three-dimensional XY model. Monte Carlo simulations and finite-size scaling are used to determine critical couplings K(c) and exponents. In agreement with experiments, clear evidence of change in the thermal critical exponents nu and alpha is found at nonzero volume fractions of impurities. These changes are explained in terms of hidden long-range correlations within disorder distributions.
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Affiliation(s)
- C Vásquez
- LFESD, Centro de Física, IVIC, Apartado 21827, Caracas 1020A, Venezuela
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Chen XS, Dohm V. Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056127. [PMID: 12786240 DOI: 10.1103/physreve.67.056127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2002] [Indexed: 05/24/2023]
Abstract
We calculate finite-size effects of the Gaussian model in a Lx(d-1) box geometry with free boundary conditions in one direction and periodic boundary conditions in d-1 directions for 2<d<4. We also consider film geometry (L--> infinity ). Finite-size scaling is found to be valid for d<3 and d>3 but logarithmic deviations from finite-size scaling are found for the free energy and energy density at the Gaussian upper borderline dimension d*=3. The logarithms are related to the vanishing critical exponent 1-alpha-nu=(d-3)/2 of the Gaussian surface energy density. The latter has a cusplike singularity in d>3 dimensions. We show that these properties are the origin of nonscaling finite-size effects in the mean spherical model with free boundary conditions in d > or =3 dimensions. At bulk T(c), in d=3 dimensions we find an unexpected nonlogarithmic violation of finite-size scaling for the susceptibility chi approximately L3 of the mean spherical model in film geometry, whereas only a logarithmic deviation chi approximately L2 ln L exists for box geometry. The result for film geometry is explained by the existence of the lower borderline dimension d(l)=3, as implied by the Mermin-Wagner theorem, that coincides with the Gaussian upper borderline dimension d*=3. For 3<d<4 we find a power-law violation of scaling chi approximately L(d-1) at bulk T(c) for box geometry and a nonscaling temperature dependence chi(surface) approximately xi(d) of the surface susceptibility above T(c). For 2<d<3 dimensions we show the validity of universal finite-size scaling for the susceptibility of the mean spherical model with free boundary conditions for both box and film geometry and calculate the corresponding universal scaling functions for T > or =T(c).
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Affiliation(s)
- X S Chen
- Institute of Theoretical Physics, Chinese Academy of Sciences, P.O. Box 2735, Beijing 100080, China
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Strösser M, Dohm V. Minimal renormalization without epsilon expansion: four-loop free energy in three dimensions for general n above and below Tc. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:056115. [PMID: 12786228 DOI: 10.1103/physreve.67.056115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2002] [Indexed: 05/24/2023]
Abstract
We present an analytic four-loop calculation of the free energy in three dimensions within the O(n) symmetric phi(4) theory at infinite cutoff for general n above and below T(c). It is shown that Goldstone singularities arising at intermediate stages of the calculation cancel among themselves. The correlation length above T(c) and an appropriately defined pseudocorrelation length below T(c) are calculated analytically up to four-loop order for general n. The method of minimal renormalization at fixed dimension d=3 is used to determine the analytic expressions for the four-loop series of the amplitude functions of the free energy, correlation length, and specific heat above and below T(c) in terms of the renormalized coupling. These expressions provide the basis for future accurate Borel resummations of universal amplitude ratios characterizing the asymptotic critical behavior and of crossover functions describing the nonasymptotic critical behavior. A brief application is given by a variational calculation of the universal specific-heat amplitude ratios A+/A- and P=alpha(-1)(1-A+/A-) and of the universal quantity R+(xi)=xi+0(A+)(1/d) for general n.
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Affiliation(s)
- M Strösser
- Institut für Theoretische Physik, Technische Hochschule Aachen, D-52056 Aachen, Germany
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Murphy D, Genio E, Ahlers G, Liu F, Liu Y. Finite-size scaling and universality of the thermal resistivity of liquid 4He near Tlambda. PHYSICAL REVIEW LETTERS 2003; 90:025301. [PMID: 12570552 DOI: 10.1103/physrevlett.90.025301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2002] [Indexed: 05/24/2023]
Abstract
We present measurements of the thermal resistivity rho(t,P,L) near the superfluid transition of 4He at saturated vapor pressure and confined in cylindrical geometries with radii L=0.5 and 1.0 microm [t identical with T/T(lambda)(P)-1]. For L=1.0 microm measurements at six pressures P are presented. At and above T(lambda) the data are consistent with a universal scaling function F(X)=(L/xi(0))(x/nu)(rho/rho(0)), X=(L/xi(0))(1/nu)t valid for all P (rho(0) and x are the pressure-dependent amplitude and effective exponent of the bulk resistivity rho, and xi=xi(0)t(-nu) is the correlation length). Indications of breakdown of scaling and universality are observed below T(lambda).
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Affiliation(s)
- Daniel Murphy
- Department of Physics and iQUEST, University of California, Santa Barbara, California 93106, USA
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17
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Folk R, Holovatch Y, Yavorskii T. Critical exponents of a three-dimensional weakly diluted quenched Ising model. ACTA ACUST UNITED AC 2003. [DOI: 10.3367/ufnr.0173.200302c.0175] [Citation(s) in RCA: 63] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/01/2022]
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18
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Cucchieri A, Engels J, Holtmann S, Mendes T, Schulze T. Universal amplitude ratios from numerical studies of the three-dimensional O(2) model. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/31/301] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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19
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Hager JS. Six-loop renormalization group functions ofO(n)-symmetric ϕ6-theory and ϵ-expansions of tricritical exponents up to ϵ3. ACTA ACUST UNITED AC 2002. [DOI: 10.1088/0305-4470/35/12/301] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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20
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Arnold P, Moore GD. Monte Carlo simulation of O(2) phi(4) field theory in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:066113. [PMID: 11736242 DOI: 10.1103/physreve.64.066113] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/13/2001] [Revised: 07/02/2001] [Indexed: 05/23/2023]
Abstract
Using standard numerical Monte Carlo lattice methods, we study non-universal properties of the phase transition of three-dimensional straight phi(4) theory of a two-component real field phi=(phi(1),phi(2)) with O(2) symmetry. Specifically, we extract the renormalized values of <phi(2)>/u and r/u(2) at the phase transition, where the continuum action of the theory is integral d(3)x[1/2/inverted Delta phi/(2) + 1 2r phi(2)+(u/4!)phi(4)]. These values have applications to calculating the phase-transition temperature of dilute or weakly interacting Bose gases (both relativistic and nonrelativistic). In passing, we also provide perturbative calculations of various O(a) lattice-spacing errors in three-dimensional O(N) scalar field theory, where a is the lattice spacing.
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Affiliation(s)
- P Arnold
- Department of Physics, University of Virginia, P.O. Box 400714, Charlottesville, Virginia 22904-4714, USA
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Kleinert H, Van den Bossche B. Three-loop critical exponents, amplitude functions, and amplitude ratios from variational perturbation theory. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:056113. [PMID: 11414967 DOI: 10.1103/physreve.63.056113] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2000] [Indexed: 05/23/2023]
Abstract
We use variational perturbation theory to calculate various universal amplitude ratios above and below Tc in minimally subtracted straight phi4 theory with N components in three dimensions. In order to best exhibit the method as a powerful alternative to Borel resummation techniques, we consider only two- and three-loops expressions where our results are analytic expressions. For the critical exponents, we also extend existing analytic expressions for two loops to three loops.
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Affiliation(s)
- H Kleinert
- Institut für Theoretische Physik, Arnimallee 14 D-14195 Berlin, Germany
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Kimball MO, Gasparini FM. Superfluid fraction of (3)He-(4)He mixtures confined at 0.0483 microm between silicon wafers. PHYSICAL REVIEW LETTERS 2001; 86:1558-1561. [PMID: 11290192 DOI: 10.1103/physrevlett.86.1558] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/12/2000] [Indexed: 05/23/2023]
Abstract
We report measurements of the superfluid fraction rho(s)/rho of films of (3)He-(4)He mixtures confined between silicon wafers at 0.0483 microm separation. The data obtained using adiabatic fountain resonance (AFR) can be used to test for the first time expectations of correlation-length scaling in the case of planar mixtures. For the mixtures, the data for rho(s)/rho collapse well on a universal function. The dissipation associated with AFR can also be scaled, and indicates two-dimensional crossover. These results are in contrast to pure (4)He, where over a wider range of confinements, the data for rho(s)/rho are found not to scale.
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Kleinert H, Schulte-Frohlinde V. Critical exponents from five-loop strong-coupling ϕ4-theory in 4-ε dimensions. ACTA ACUST UNITED AC 2001. [DOI: 10.1088/0305-4470/34/5/308] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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