Link overlaps at Criticality and Universality in Ising Spin Glasses

TL;DR

This study uses extensive simulations to analyze link and spin overlaps in high-dimensional Ising Spin Glasses, revealing critical behavior and non-universality of critical exponents depending on interaction distributions.

Contribution

It demonstrates that link overlaps are effective for identifying phase transitions and shows that critical exponents vary with the interaction distribution, challenging universality.

Findings

Link overlaps exhibit clear critical behavior near transition temperature.

Link overlaps are more efficient than spin overlaps for transition detection.

Critical exponents differ between bimodal and Gaussian distributions in 4D and 5D.

Abstract

Extensive simulations are made of link and spin overlaps in four and five dimensional Ising Spin Glasses (ISGs). Moments and moment ratios of the mean link overlap distributions (the variance, the kurtosis and the skewness) show clear critical behavior around the ISG ordering temperature. The link overlap measurements can be used to identify the ISG transition accurately; the link overlap is often a more efficient tool in this context than the spin overlap because the link overlap inter-sample variability is much weaker. Once the transition temperature is accurately established, critical exponents can be readily estimated by extrapolating measurements made in the thermodynamic limit regime. The data show that the bimodal and Gaussian spin glass susceptibility exponents $\gamma$ are different from each other, both in dimension 5 and in dimension 4. Hence ISG critical exponents are not universal in a given dimension, but depend on the form of the interaction distribution.