Evidence for non-universal scaling in dimension four Ising spin glasses

TL;DR

This study investigates the critical behavior of four-dimensional Ising spin glasses, revealing non-universal scaling behavior between different interaction models through simulation analysis of the Binder cumulant.

Contribution

It provides the first detailed comparison of the Binder cumulant's critical limit in bimodal and Laplacian interaction models in four dimensions, highlighting non-universality.

Findings

Critical limit for bimodal model: 0.523(3)

Critical limit for Laplacian model: 0.473(3)

Evidence of non-universal scaling in 4D spin glasses

Abstract

The critical behavior of the Binder cumulant for Ising spin glasses in dimension four are studied through simulation measurements. Data for the bimodal interaction model are compared with those for the Laplacian interaction model. Special attention is paid to scaling corrections. The limiting infinite size value at criticality for this dimensionless variable is a parameter characteristic of a universality class. This critical limit is estimated to be equal to $0.523(3)$ in the bimodal model and to $0.473(3)$ in the Laplacian model.