The Ising Spin Glass in dimension four

TL;DR

This paper investigates the critical behaviors of four-dimensional bimodal and Gaussian Ising spin glass models through extensive simulations and high temperature series expansion analysis, revealing distribution-dependent critical exponents.

Contribution

It provides the first comprehensive comparison of critical exponents and constants for different interaction distributions in 4D ISG models using both simulations and HTSE data.

Findings

Critical exponents depend on the interaction distribution.

HTSE estimates agree with simulation results.

Critical temperatures are accurately determined from HTSE.

Abstract

The critical behaviors of the bimodal and Gaussian Ising spin glass (ISG) models in dimension four are studied through extensive numerical simulations, and from an analysis of high temperature series expansion (HTSE) data of Klein {\it et al.} (1991). The simulations include standard finite size scaling measurements, thermodynamic limit regime measurements, and analyses which provide estimates of critical exponents without any consideration of the critical temperature. The higher order HTSE series for the bimodal model provide accurate estimates of the critical temperature and critical exponents. These estimates are independent of and fully consistent with the simulation values. Comparisons between ISG models in dimension four show that the critical exponents and the critical constants for dimensionless observables depend on the form of the interaction distribution of the model.