Monte Carlo Simulation of the Three-dimensional Ising Spin Glass

TL;DR

This paper uses Monte Carlo simulations to analyze the 3D Ising spin glass, providing evidence for finite-size scaling and exploring the nature of the phase transition, including the possibility of a continuous transition or an essential singularity.

Contribution

It offers the first detailed finite-size scaling analysis of the 3D Ising spin glass with universal scaling functions and extrapolates data to infinite volume.

Findings

Finite-size scaling functions are determined.

Data are consistent with a continuous phase transition or an essential singularity.

An essential singularity at zero temperature is excluded.

Abstract

We study the 3D Edwards-Anderson model with binary interactions by Monte Carlo simulations. Direct evidence of finite-size scaling is provided, and the universal finite-size scaling functions are determined. Using an iterative extrapolation procedure, Monte Carlo data are extrapolated to infinite volume up to correlation length \xi = 140. The infinite volume data are consistent with both a continuous phase transition at finite temperature and an essential singularity at finite temperature. An essential singularity at zero temperature is excluded.