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Marín Ramírez JM, Oblak E, Riego P, Campillo G, Osorio J, Arnache O, Berger A. Experimental exploration of dynamic phase transitions and associated metamagnetic fluctuations for materials with different Curie temperatures. Phys Rev E 2020; 102:022804. [PMID: 32942401 DOI: 10.1103/physreve.102.022804] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2020] [Accepted: 07/28/2020] [Indexed: 11/07/2022]
Abstract
We study dynamic magnetic behavior in the vicinity of the dynamic phase transition (DPT) for a suitable series of samples that have different Curie temperatures T_{C}, which thus enables us to experimentally explore the role of the reduced temperature T/T_{C} in the DPT. For this purpose, we fabricate Co_{1-x}Ru_{x} epitaxial thin films with uniaxial in-plane anisotropy by means of sputter deposition in the concentration range 0.0≤x≤0.26. All samples are ferromagnetic at room temperature, exhibit an abrupt magnetization reversal along their easy axis, and represent a unique T_{C} and thus T/T_{C} ratio according to their Ru concentration. The dynamic magnetic behavior is measured by using an ultrasensitive transverse magneto-optical detection method and the resulting dynamic states are explored as a function of the applied magnetic field amplitude H_{0} and period P, as well as an additional bias field H_{b}, which is the conjugate field of the dynamic order parameter Q. Our experimental results demonstrate that the qualitative behavior of the dynamic phase diagram is independent of the T/T_{C} ratio and that for all T/T_{C} values we observe metamagnetic anomalies in the dynamic paramagnetic state, which do not exist in the corresponding thermodynamic phase diagram. However, quantitatively, these metamagnetic anomalies are very strongly dependent on the T/T_{C} ratio, leading to an about 20-fold increase of large metamagnetic fluctuations in the paramagnetic regime as the T/T_{C} ratio increases from 0.37 to 0.68. Also, the phase space range in which these anomalous metamagnetic fluctuations occur extends closer and closer to the critical point as T/T_{C} increases.
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Affiliation(s)
- J M Marín Ramírez
- CIC nanoGUNE BRTA, 20018 Donostia - San Sebastián, Spain.,Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Apartado Aéreo 1226, Medellín, Colombia
| | - E Oblak
- CIC nanoGUNE BRTA, 20018 Donostia - San Sebastián, Spain
| | - P Riego
- CIC nanoGUNE BRTA, 20018 Donostia - San Sebastián, Spain.,Departamento de Física de la Materia Condensada, Universidad del País Vasco (UPV/EHU), 48080 Bilbao, Spain
| | - G Campillo
- Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia
| | - J Osorio
- Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Apartado Aéreo 1226, Medellín, Colombia
| | - O Arnache
- Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Apartado Aéreo 1226, Medellín, Colombia
| | - A Berger
- CIC nanoGUNE BRTA, 20018 Donostia - San Sebastián, Spain
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Park H, Pleimling M. Surface criticality at a dynamic phase transition. PHYSICAL REVIEW LETTERS 2012; 109:175703. [PMID: 23215204 DOI: 10.1103/physrevlett.109.175703] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/22/2012] [Indexed: 06/01/2023]
Abstract
In order to elucidate the role of surfaces at nonequilibrium phase transitions, we consider kinetic Ising models with surfaces subjected to a periodic oscillating magnetic field. Whereas, the corresponding bulk system undergoes a continuous nonequilibrium phase transition characterized by the exponents of the equilibrium Ising model, we find that the nonequilibrium surface exponents do not coincide with those of the equilibrium critical surface. In addition, in three space dimensions, the surface phase diagram of the nonequilibrium system differs markedly from that of the equilibrium system.
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Affiliation(s)
- Hyunhang Park
- Department of Physics, Virginia Tech, Blacksburg, Virginia 24060-0435, USA
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Vargunin A, Ord T, Tammelo R. Complementarity of phase transition and stochastic resonance in spatially restricted systems. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:061137. [PMID: 18643247 DOI: 10.1103/physreve.77.061137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2007] [Indexed: 05/26/2023]
Abstract
We study the linear response in a soft potential, the Landau-type temperature dependence of which is responsible for the monostable-to-bistable transformation. The system can be considered as a model of a sample with internal noise, where a second-order phase transition takes place in the bulk limit. The intensity of noise influencing the order parameter is supposed to be a function of the volume. We demonstrate that the anomaly of susceptibility at the phase transition point described by the Landau phase transition theory transforms into the maximal response caused by stochastic resonance if the volume of the system decreases. The phenomenon can be treated also as an increase in the diffuseness of a phase transition with lowering of the critical temperature. We suggest that it is this crossover that contributes to the mechanism of dielectric peculiarities in ceramic and relaxor ferroelectrics.
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Affiliation(s)
- Artjom Vargunin
- Institute of Theoretical Physics, University of Tartu, 4 Tähe Street, Tartu, Estonia
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Bordogna CM, Albano EV. Dynamic behavior of a social model for opinion formation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:061125. [PMID: 18233832 DOI: 10.1103/physreve.76.061125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/31/2007] [Indexed: 05/25/2023]
Abstract
The dynamic behavior of a social group influenced by both a strong leader and the mass media, which is modeled according to the social impact theory, is studied under two situations: (i) The strong leader changes his/her state of opinion periodically while the mass media are not considered. In this case, the leader is capable of driving the group between a dynamically ordered state with a weak leader-group coupling (high-frequency regime) and a dynamically disordered state where the group follows the opinion of the leader (low-frequency regime). (ii) The mass-media change periodically their message and have to compete with a strong leader that keeps his/her state of opinion unchanged. In this case, the mass media require an amplitude threshold in order to overcome the influence of the leader and drive the system into a dynamically disordered state. The dynamic behavior characteristic of the studied social opinion model shares many features of physical systems that are relevant in the fields of statistical mechanics and condensed matter.
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Affiliation(s)
- Clelia M Bordogna
- IMApEC, Facultad de Ingeniería, UNLP, Calle 115 Esquina 50, (1900) La Plata, Argentina
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Robb DT, Rikvold PA, Berger A, Novotny MA. Conjugate field and fluctuation-dissipation relation for the dynamic phase transition in the two-dimensional kinetic Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:021124. [PMID: 17930023 DOI: 10.1103/physreve.76.021124] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2007] [Indexed: 05/25/2023]
Abstract
The two-dimensional kinetic Ising model, when exposed to an oscillating applied magnetic field, has been shown to exhibit a nonequilibrium, second-order dynamic phase transition (DPT), whose order parameter Q is the period-averaged magnetization. It has been established that this DPT falls in the same universality class as the equilibrium phase transition in the two-dimensional Ising model in zero applied field. Here we study the scaling of the dynamic order parameter with respect to a nonzero, period-averaged, magnetic "bias" field, H(b) for a DPT produced by a square-wave applied field. We find evidence that the scaling exponent, delta(d), of H(b) at the critical period of the DPT is equal to the exponent for the critical isotherm, delta(e), in the equilibrium Ising model. This implies that H(b) is a significant component of the field conjugate to Q. A finite-size scaling analysis of the dynamic order parameter above the critical period provides further support for this result. We also demonstrate numerically that, for a range of periods and values of H(b) in the critical region, a fluctuation-dissipation relation (FDR), with an effective temperature T(eff)(T,P,H0) depending on the period, and possibly the temperature and field amplitude, holds for the variables Q and H(b). This FDR justifies the use of the scaled variance of Q as a proxy for the nonequilibrium susceptibility, partial differential Q/partial differential H(b), in the critical region.
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Affiliation(s)
- D T Robb
- School of Computational Science, Florida State University, Tallahassee, Florida 32306, USA.
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Fujiwara N, Kobayashi T, Fujisaka H. Dynamic phase transition in a rotating external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:026202. [PMID: 17358400 DOI: 10.1103/physreve.75.026202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2006] [Indexed: 05/14/2023]
Abstract
Dynamic phase transition in the Ginzburg-Landau model of the anisotropic XY spin system in a rotating external field is studied. We observe several types of oscillations, limit cycles, quasiperiodic oscillations and chaotic motions. It is found that limit cycle oscillations can have the periodicity of multiple times of the period of the applied field and that the system shows two kinds of scenarios leading to the onset of quasiperiodic oscillations, i.e., the saddle-node and Hopf bifurcations. Furthermore, this paper reports the findings of chaotic behaviors in the context of dynamic phase transition and that there exist two types of chaos with and without a certain kind of symmetry.
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Affiliation(s)
- Naoya Fujiwara
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
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Keskin M, Canko O, Deviren B. Dynamic phase transition in the kinetic spin- Blume-Capel model under a time-dependent oscillating external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011110. [PMID: 16907063 DOI: 10.1103/physreve.74.011110] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2006] [Indexed: 05/11/2023]
Abstract
We present a study, within a mean-field approach, of the stationary states of the kinetic spin-3/2 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization (m) of the system oscillates in time around zero, which corresponds to a paramagnetic phase (P), and an antisymmetric one where m oscillates in time around a finite value different from zero, namely +/-3/2 and +/-1/2 that corresponds to the ferromagnetic-3/2 (F3/2) and the ferromagnetic-1/2 (F1/2) phases, respectively. There are coexistence regions of the phase space where the F3/2, F1/2, (F3/2 + F1/2), F3/2, P(F3/2 + P), F1/2, and P(F1/2 + P), F3/2, F1/2, P(F3/2 + F1/2 + P) phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.
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Affiliation(s)
- Mustafa Keskin
- Department of Physics, Erciyes University, 38039 Kayseri, Turkey
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Machado E, Buendía GM, Rikvold PA, Ziff RM. Response of a catalytic reaction to periodic variation of the CO pressure: increased CO2 production and dynamic phase transition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 71:016120. [PMID: 15697671 DOI: 10.1103/physreve.71.016120] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2004] [Indexed: 05/24/2023]
Abstract
We present a kinetic Monte Carlo study of the dynamical response of a Ziff-Gulari-Barshad model for CO oxidation with CO desorption to periodic variation of the CO pressure. We use a square-wave periodic pressure variation with parameters that can be tuned to enhance the catalytic activity. We produce evidence that, below a critical value of the desorption rate, the driven system undergoes a dynamic phase transition between a CO2 productive phase and a nonproductive one at a critical value of the period and waveform of the pressure oscillation. At the dynamic phase transition the period-averaged CO2 production rate is significantly increased and can be used as a dynamic order parameter. We perform a finite-size scaling analysis that indicates the existence of power-law singularities for the order parameter and its fluctuations, yielding estimated critical exponent ratios beta/nu approximately 0.12 and gamma/nu approximately 1.77. These exponent ratios, together with theoretical symmetry arguments and numerical data for the fourth-order cumulant associated with the transition, give reasonable support for the hypothesis that the observed nonequilibrium dynamic phase transition is in the same universality class as the two-dimensional equilibrium Ising model.
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Affiliation(s)
- Erik Machado
- Physics Department, Universidad Simón Bolívar, Apartado 89000, Caracas 1080, Venezuela
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Fujiwara N, Tutu H, Fujisaka H. Magnetic walls in the anisotropic XY-spin system in an oscillating magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:066132. [PMID: 15697459 DOI: 10.1103/physreve.70.066132] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/17/2004] [Indexed: 05/24/2023]
Abstract
Wall structures associated with dynamic phase transitions in the anisotropic XY -spin system in a temporally oscillating magnetic field h cos (Omegat) in a one-dimensional system are analyzed by using the time-dependent Ginzburg-Landau model. It is numerically confirmed that there exist two types of magnetic walls, i.e., the Néel and Bloch walls, and is found that the transition between the two walls can occur for changing h or Omega . The phase diagram for the stable regions of each wall is obtained by both numerical and analytical methods. Furthermore, the critical behavior of the modulus of the Bloch wall around the Néel-Bloch transition point is studied, and it is found that the transition can be either continuous or discontinuous with respect to h, depending on Omega .
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Affiliation(s)
- Naoya Fujiwara
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.
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Jang H, Grimson MJ, Woolf TB. Stochastic dynamics and the dynamic phase transition in thin ferromagnetic films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:047101. [PMID: 15600564 DOI: 10.1103/physreve.70.047101] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2004] [Indexed: 05/24/2023]
Abstract
The dynamic phase behavior of a classical Heisenberg spin system with a bilinear exchange anisotropy in a planar thin film geometry has been investigated by Monte Carlo simulations using different forms for the stochastic dynamics. In simulations of the dynamic phase transition (DPT) in films subject to a pulsed oscillatory external field with competing surface fields, both Glauber and Metropolis dynamics show a continuous DPT. But while the field amplitude dependence of the DPT is similar in both cases, the transition region for the DPT as a function of temperature is more extended with Metropolis dynamics. The difference arises from a decoupling of the surface and bulk responses of the film near the dynamic phase transition with Metropolis dynamics that is not evident for Glauber dynamics.
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Affiliation(s)
- Hyunbum Jang
- Department of Physiology, Johns Hopkins University, Baltimore, Maryland 21205, USA
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Jang H, Grimson MJ, Hall CK. Exchange anisotropy and the dynamic phase transition in thin ferromagnetic Heisenberg films. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:046115. [PMID: 14683010 DOI: 10.1103/physreve.68.046115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/14/2003] [Indexed: 05/24/2023]
Abstract
Monte Carlo simulations have been performed to investigate the dependence of the dynamic phase behavior on the bilinear exchange anisotropy of a classical Heisenberg spin system. The system under consideration is a planar thin ferromagnetic film with competing surface fields subject to a pulsed oscillatory external field. The results show that the films exhibit a single discontinuous dynamic phase transition (DPT) as a function of the anisotropy of the bilinear exchange interaction in the Hamiltonian. Furthermore, there is no evidence of stochastic resonance associated with the DPT. These results are in marked contrast to the continuous DPT observed in the same system as a function of temperature and applied field strength for a fixed bilinear exchange anisotropy.
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Affiliation(s)
- Hyunbum Jang
- Department of Physiology, Johns Hopkins University, Baltimore, Maryland 21205, USA
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Korniss G, Rikvold PA, Novotny MA. Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:056127. [PMID: 12513576 DOI: 10.1103/physreve.66.056127] [Citation(s) in RCA: 35] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2002] [Indexed: 05/24/2023]
Abstract
It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is of the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit, the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.
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Affiliation(s)
- G Korniss
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York 12180-3590, USA.
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Yasui T, Tutu H, Yamamoto M, Fujisaka H. Dynamic phase transitions in the anisotropic XY spin system in an oscillating magnetic field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2002; 66:036123. [PMID: 12366200 DOI: 10.1103/physreve.66.036123] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/19/2002] [Indexed: 05/23/2023]
Abstract
The Ginzburg-Landau model for the anisotropic XY spin system in an oscillating magnetic field below the critical temperature T(c), psi;(r,t)=(T(c)-T)psi-/psi/(2)psi+gammapsi(*)+ nabla (2)psi+h cos(Omegat) is both theoretically and numerically studied. Here psi is the complex order parameter and gamma stands for the real anisotropy parameter. It is numerically shown that the spatially uniform system shows various characteristic oscillations (dynamical phases), depending on the amplitude h and the frequency Omega of the external field. As the control parameter, either h or Omega, is changed, there exist dynamical phase transitions (DPT), separating them. By making use of the mode expansion analysis, we obtain the phase diagrams, which turn out to be in a qualitative agreement with the numerically obtained ones. By carrying out the Landau expansion, the reduced equations of motion near the DPT are derived. Furthermore, taking into account the spatial variation of order parameters, we will derive the analytic expressions for domain walls, which are represented by the Néel and Bloch type walls, depending on the difference of the coexistence of phases.
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Affiliation(s)
- Tomoaki Yasui
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University, Japan.
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