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Vedula B, Moore MA, Sharma A. Study of the de Almeida-Thouless line in the one-dimensional diluted power-law XY spin glass. Phys Rev E 2023; 108:014116. [PMID: 37583164 DOI: 10.1103/physreve.108.014116] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/09/2023] [Accepted: 06/21/2023] [Indexed: 08/17/2023]
Abstract
We study the de Almeida-Thouless (AT) line in the one-dimensional power-law diluted XY spin-glass model, in which the probability that two spins separated by a distance r interact with each other, decays as 1/r^{2σ}. Tuning the exponent σ is equivalent to changing the space dimension of a short-range model. We develop a heat bath algorithm to equilibrate XY spins; using this in conjunction with the standard parallel tempering and overrelaxation sweeps, we carry out large-scale Monte Carlo simulations. For σ=0.6, which is in the mean-field regime above six dimensions-it is similar to being in 10 dimensions-we find clear evidence for an AT line. For σ=0.75 and σ=0.85, which are in the non-mean-field regime and similar to four and three dimensions, respectively, our data is like that found in previous studies of the Ising and Heisenberg spin glasses when reducing the temperature at fixed field. For σ=0.75, there is evidence from finite-size-scaling studies for an AT transition but for σ=0.85, the evidence for a transition is nonexistent. We have also studied these systems at fixed temperature varying the field and discovered that at both σ=0.75 and at σ=0.85 there is evidence of an AT transition! Confusingly, the correlation length and spin-glass susceptibility as a function of the field are both entirely consistent with the predictions of the droplet picture and hence the nonexistence of an AT line. In the usual finite-size critical point scaling studies used to provide evidence for an AT transition, there is seemingly good evidence for an AT line at σ=0.75 for small values of the system size N, which is strengthening as N is increased, but for N>2048 the trend changes and the evidence then weakens as N is further increased. We have also studied with fewer bond realizations the system at σ=0.70, which is the analog of a system with short-range interactions just below six dimensions, and found that it is similar in its behavior to the system at σ=0.75 but with larger finite-size corrections. The evidence from our simulations points to the complete absence of the AT line in dimensions outside the mean-field region and to the correctness of the droplet picture. Previous simulations which suggested there was an AT line can be attributed to the consequences of studying systems which are just too small. The collapse of our data to the droplet scaling form is poor for σ=0.75 and to some extent also for σ=0.85, when the correlation length becomes of the order of the length of the system, due to the existence of excitations which only cost a free energy of O(1), just as envisaged in the TNT picture of the ordered state of spin glasses. However, for the case of σ=0.85 we can provide evidence that for larger system sizes, droplet scaling will prevail even when the correlation length is comparable to the system size.
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Affiliation(s)
- Bharadwaj Vedula
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India
| | - M A Moore
- Department of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Auditya Sharma
- Department of Physics, Indian Institute of Science Education and Research, Bhopal, Madhya Pradesh 462066, India
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Hong W, Liu L, Liu C, Ma X, Koda A, Li X, Song J, Yang W, Yang J, Cheng P, Zhang H, Bao W, Ma X, Chen D, Sun K, Guo W, Luo H, Sandvik AW, Li S. Extreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet. PHYSICAL REVIEW LETTERS 2021; 126:037201. [PMID: 33543946 DOI: 10.1103/physrevlett.126.037201] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/26/2020] [Revised: 10/16/2020] [Accepted: 01/04/2021] [Indexed: 06/12/2023]
Abstract
Sr_{2}CuTeO_{6} is a square-lattice Néel antiferromagnet with superexchange between first-neighbor S=1/2 Cu spins mediated by plaquette centered Te ions. Substituting Te by W, the affected impurity plaquettes have predominantly second-neighbor interactions, thus causing local magnetic frustration. Here we report a study of Sr_{2}CuTe_{1-x}W_{x}O_{6} using neutron diffraction and μSR techniques, showing that the Néel order vanishes already at x=0.025±0.005. We explain this extreme order suppression using a two-dimensional Heisenberg spin model, demonstrating that a W-type impurity induces a deformation of the order parameter that decays with distance as 1/r^{2} at temperature T=0. The associated logarithmic singularity leads to loss of order for any x>0. Order for small x>0 and T>0 is induced by weak interplane couplings. In the nonmagnetic phase of Sr_{2}CuTe_{1-x}W_{x}O_{6}, the μSR relaxation rate exhibits quantum critical scaling with a large dynamic exponent, z≈3, consistent with a random-singlet state.
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Affiliation(s)
- Wenshan Hong
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Lu Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
| | - Chang Liu
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Xiaoyan Ma
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
| | - Akihiro Koda
- Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK-IMSS),1-1 Oho, Tsukuba 305-0801, Japan
- Department of Materials Structure Science, Sokendai (The Graduate University for Advanced Studies), Tsukuba, Ibaraki, 305-0801, Japan
| | - Xin Li
- Key Laboratory of Neutron Physics and Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621999, China
| | - Jianming Song
- Key Laboratory of Neutron Physics and Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics, Mianyang 621999, China
| | - Wenyun Yang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
| | - Jinbo Yang
- State Key Laboratory for Mesoscopic Physics, School of Physics, Peking University, Beijing, 100871, China
| | - Peng Cheng
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 1 00872, China
| | - Hongxia Zhang
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 1 00872, China
| | - Wei Bao
- Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 1 00872, China
- Department of Physics, City Univesity of Hong Kong, Kowloon, Hong Kong
| | - Xiaobai Ma
- Department of Nuclear Physics, China Institute of Atomic Energy, Beijing, 102413, China
| | - Dongfeng Chen
- Department of Nuclear Physics, China Institute of Atomic Energy, Beijing, 102413, China
| | - Kai Sun
- Department of Nuclear Physics, China Institute of Atomic Energy, Beijing, 102413, China
| | - Wenan Guo
- Department of Physics, Beijing Normal University, Beijing 100875, China
- Beijing Computational Science Research Center, Beijing 100193, China
| | - Huiqian Luo
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
| | - Anders W Sandvik
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA
| | - Shiliang Li
- Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
- School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, China
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Mitsumoto K, Hotta C, Yoshino H. Spin-Orbital Glass Transition in a Model of a Frustrated Pyrochlore Magnet without Quenched Disorder. PHYSICAL REVIEW LETTERS 2020; 124:087201. [PMID: 32167313 DOI: 10.1103/physrevlett.124.087201] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2019] [Revised: 12/09/2019] [Accepted: 01/21/2020] [Indexed: 06/10/2023]
Abstract
We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y_{2}Mo_{2}O_{7}, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical disorder for each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielectric nonlinear susceptibilities, resolving the long-standing puzzle on the origin of the disorder-free spin glass.
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Affiliation(s)
- Kota Mitsumoto
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
| | - Chisa Hotta
- Department of Basic Science, University of Tokyo, Tokyo 153-8902, Japan
| | - Hajime Yoshino
- Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
- Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan
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Andrade EC, Hoyos JA, Rachel S, Vojta M. Cluster-Glass Phase in Pyrochlore XY Antiferromagnets with Quenched Disorder. PHYSICAL REVIEW LETTERS 2018; 120:097204. [PMID: 29547304 DOI: 10.1103/physrevlett.120.097204] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2017] [Indexed: 06/08/2023]
Abstract
We study the impact of quenched disorder (random exchange couplings or site dilution) on easy-plane pyrochlore antiferromagnets. In the clean system, order by disorder selects a magnetically ordered state from a classically degenerate manifold. In the presence of randomness, however, different orders can be chosen locally depending on details of the disorder configuration. Using a combination of analytical considerations and classical Monte Carlo simulations, we argue that any long-range-ordered magnetic state is destroyed beyond a critical level of randomness where the system breaks into magnetic domains due to random exchange anisotropies, becoming, therefore, a glass of spin clusters, in accordance with the available experimental data. These random anisotropies originate from off-diagonal exchange couplings in the microscopic Hamiltonian, establishing their relevance to other magnets with strong spin-orbit coupling.
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Affiliation(s)
- Eric C Andrade
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, São Paulo 13560-970, Brazil
| | - José A Hoyos
- Instituto de Física de São Carlos, Universidade de São Paulo, C.P. 369, São Carlos, São Paulo 13560-970, Brazil
| | - Stephan Rachel
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
- School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
| | - Matthias Vojta
- Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany
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Shinaoka H, Tomita Y, Motome Y. Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice. PHYSICAL REVIEW LETTERS 2011; 107:047204. [PMID: 21867037 DOI: 10.1103/physrevlett.107.047204] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/2010] [Revised: 05/07/2011] [Indexed: 05/31/2023]
Abstract
Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate the effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature T(f) is largely enhanced by the spin-lattice coupling and, furthermore, becomes almost independent of Δ in a wide range of the disorder strength Δ. The critical property of the spin-glass transition is indistinguishable from that of the canonical Heisenberg spin glass in the entire range of Δ. These peculiar behaviors are ascribed to a modification of the degenerate manifold from a continuous to semidiscrete one by spin-lattice coupling.
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Affiliation(s)
- Hiroshi Shinaoka
- Institute for Solid State Physics, University of Tokyo, Kashiwanoha, Kashiwa, Chiba, 277-8581, Japan
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Campos I, Cotallo-Aban M, Martin-Mayor V, Perez-Gaviro S, Tarancon A. Spin-glass transition of the three-dimensional Heisenberg spin glass. PHYSICAL REVIEW LETTERS 2006; 97:217204. [PMID: 17155771 DOI: 10.1103/physrevlett.97.217204] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/22/2006] [Indexed: 05/12/2023]
Abstract
It is shown, by means of Monte Carlo simulation and finite size scaling analysis, that the Heisenberg spin glass undergoes a finite-temperature phase transition in three dimensions. There is a single critical temperature, at which both a spin glass and a chiral glass ordering develop. The Monte Carlo algorithm, adapted from lattice gauge theory simulations, makes it possible to thermalize lattices of size L = 32, larger than in any previous spin-glass simulation in three dimensions. High accuracy is reached thanks to the use of the Marenostrum supercomputer. The large range of system sizes studied allows us to consider scaling corrections.
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Affiliation(s)
- I Campos
- Instituto de Biocomputación y Física de Sistemas Complejos (BIFI), Corona de Aragón 42, Zaragoza 50009, Spain
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