Numerical Simulations of Spin Glass Systems

TL;DR

This paper reviews Monte Carlo simulation techniques applied to finite-dimensional spin glass systems, analyzing their phases, critical behavior, and out-of-equilibrium dynamics across different dimensions.

Contribution

It provides a comprehensive overview of simulation results and theoretical insights into spin glass phases, including ultrametric structure and dynamics in 2D, 3D, and 4D.

Findings

Identification of phase behavior in 3D spin glasses

Analysis of ultrametric structure and dynamics

Comparison of spin glass properties across dimensions

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.