Numerical Simulations of Spin Glass Systems

Abstract

We discuss the status of Monte Carlo simulations of (mainly finite dimensional) spin glass systems. After a short historical note and a brief theoretical introduction we start by discussing the (crucial) 3D case: the warm phase, the critical point and the cold phase, the ultrametric structure and the out of equilibrium dynamics. With the same style we discuss the cases of 4D and 2D. In a few appendices we give some details about the definition of states and about the tempering Monte Carlo approach.

Contribution to the volume: "Spin Glasses and Random Fields", edited by P. Young. 40 pages including 13 figures

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• On the Phase Structure of the 3D Edwards Anderson Spin Glass
• Domain-Wall Free-Energy of Spin Glass Models:Numerical Method and Boundary Conditions
• Random Fixed Point of Three-Dimensional Random-Bond Ising Models
• Replica Symmetry Breaking in Bipartite Spin Glasses and Neural Networks
• Small Window Overlaps Are Effective Probes of Replica Symmetry Breaking in 3D Spin Glasses
• Critical Behavior of the 4D Spin Glass in Magnetic Field
• Real Space Migdal-Kadanoff Renormalisation of Glassy Systems: Recent Results and a Critical Assessment
• Replica symmetric spin glass field theory
• Off-equilibrium fluctuation-dissipation relations in the 3d Ising Spin Glass in a magnetic field
• Tempering simulations in the four dimensional +-J Ising spin glass in a magnetic field
• Numerical Evidence for Continuity of Mean Field and Finite Dimensional Spin Glasses
• Calculation of the Residual Entropy of Ice Ih by Monte Carlo simulation with the Combination of the Replica-Exchange Wang-Landau algorithm and Multicanonical Replica-Exchange Method
• Off-Equilibrium Dynamics of a 4D Spin Glass with Asymmetric Couplings
• Crossovers in the Two Dimensional Ising Spin Glass with ferromagnetic next-nearest-neighbor interactions
• On the replica approach to glasses
• Self-Avoiding Random Dynamics on Integer Complex Systems
• Enhanced Sampling Algorithms
• Optimal Allocation of Replicas to Processors in Parallel Tempering Simulations