Universal Finite Size Scaling Functions in the 3D Ising Spin Glass

TL;DR

This study investigates the finite-size scaling behavior of the 3D Edwards-Anderson spin glass model using Monte Carlo simulations, identifying universal scaling functions and estimating critical parameters.

Contribution

It provides the first direct evidence of universal finite-size scaling functions in the 3D Ising spin glass and estimates critical exponents and temperature.

Findings

Finite-size scaling functions are universal.

Critical temperature estimated as Tc ≈ 1.156.

Critical exponents nu ≈ 1.8, eta ≈ -0.26.

Abstract

We study the three-dimensional 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. Monte Carlo data are extrapolated to infinite volume with an iterative procedure up to correlation lengths xi \approx 140. The infinite volume data are consistent with a conventional power law singularity at finite temperature Tc. Taking into account corrections to scaling, we find Tc = 1.156 +/- 0.015, nu = 1.8 +/- 0.2 and eta = -0.26 +/- 0.04. The data are also consistent with an exponential singularity at finite Tc, but not with an exponential singularity at zero temperature.