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Journal of Physics Conference Series

Some recent results concerning phase transitions in spin glasses

A. P. Young

Published Jan 1, 2008• 5 citations
Publisher

Abstract

I give an introduction to spin glasses, including a short discussion of experiments and theoretical concepts. I then discuss recent results from Monte Carlo simulation about two topics (i) the transition in a Heisenberg spin glass, and (ii) the transition in a magnetic field (Almeida-Thouless line) for an Ising spin glass.
DOI
10.1088/1742-6596/95/1/012003

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Some recent progress in Monte Carlo simulations of spin glasses will be presented. The problem of slow dynamics at low temperatures is partially alleviated by use of the parallel tempering (replica exchange) method. A useful technique to check for equilibration (applicable only for a Gaussian distribution) will be discussed. It will be argued that a finite size scaling analysis of the scaled correlation length of the system is a good approach with which to investigate phase transitions in spin glasses. This method will be used to study two questions: (i) whether there is a phase transition in zero field in the Heisenberg spin glass in three dimensions, and (ii) whether there is phase transition in a magnetic field in an Ising spin glass, also in three dimensions.
This thesis addresses the surprising features of zero-temperature statics and dynamics of several spin glass models, including correlations between soft spins that arise spontaneously during avalanches, and the discovery of localized states that involve the presence of two-level systems. It also presents the only detailed historiographical research on the spin glass theory. Despite the extreme simplicity of their definition, spin glasses display a wide variety of non-trivial behaviors that are not yet fully understood. In this thesis the author sheds light on some of these, focusing on both the search for phase transitions under perturbations of Hamiltonians and the zero-temperature properties and responses to external stimuli. After introducing spin glasses and useful concepts on phase transitions and numerics, the results of two massive Monte Carlo campaigns on three-dimensional systems are presented: The first of these examines the de Almeida Thouless transition, and proposes a new finite-size scaling ansatz, which accelerates the convergence to the thermodynamic limit. The second reconstructs the phase diagram of the Heisenberg spin glass with random exchange anisotropy
We show how the recent computer simulation data reported by Caracciolo et al. for the three-dimensional ±\pm± JJJ Ising spin glass in a uniform magnetic field are, in contrast to their claims, quite consistent with the simple scaling or droplet theory developed by McMillan, Fisher and Huse, and Bray and Moore, and do notnotnot provide evidence for a de Almeida-Thouless transition.
In a section of a recent paper [Phys. Rev. B 91, 104432 (2015)], the authors discuss some of the arguments in the paper by Parisi and Temesv\'ari [Nucl. Phys. B 858, 293 (2012)]. In this Comment, it is shown how these arguments are misinterpreted and the existence of the Almeida-Thouless transition in\mathit{in}in the upper critical dimension six reasserted.