Critical behavior and universality in Levy spin glasses

TL;DR

This study demonstrates that Levy-distributed spin glasses exhibit the same critical behavior as Gaussian-distributed ones, using advanced Monte Carlo simulations and extended scaling techniques to confirm universality.

Contribution

The paper provides the first large-scale numerical evidence that Levy spin glasses belong to the same universality class as Gaussian spin glasses, despite large corrections to scaling.

Findings

Critical exponents match Gaussian spin glasses

Critical temperature dependence aligns with analytical predictions

Large corrections to scaling observed in Levy spin glasses

Abstract

Using large-scale Monte Carlo simulations that combine parallel tempering with specialized cluster updates, we show that Ising spin glasses with Levy-distributed interactions share the same universality class as Ising spin glasses with Gaussian or bimodal-distributed interactions. Corrections to scaling are large for Levy spin glasses. In order to overcome these and show that the critical exponents agree with the Gaussian case, we perform an extended scaling of the two-point finite size correlation length and the spin glass susceptibility. Furthermore, we compute the critical temperature and compare its dependence on the disorder distribution width to recent analytical predictions [J. Stat. Mech. (2008) P04006].