The Ising ferromagnet in dimension five: link and spin overlaps

TL;DR

This study investigates link and spin overlap distributions in a five-dimensional Ising ferromagnet, revealing critical behaviors at the transition temperature and suggesting broader implications for ferromagnets and spin glasses.

Contribution

It introduces the measurement of link and spin overlaps in high-dimensional ferromagnets, a method previously common in spin glasses, and analyzes their critical behavior.

Findings

Overlap distributions show clear critical behavior at the transition temperature.

Moments like kurtosis and skewness peak at criticality.

Results have implications for understanding spin glasses and ferromagnetic transitions.

Abstract

In the simple [hyper]cubic five dimension near neighbor interaction Ising ferromagnet, extensive simulation measurements are made of the link overlap and the spin overlap distributions. These "two replica" measurements are standard in the Spin Glass context but are not usually recorded in ferromagnet simulations. The moments and moment ratios of these distributions (the variance, the kurtosis and the skewness) show clear critical behaviors at the known ordering temperature of the ferromagnet. Analogous overlap effects can be expected quite generally in Ising ferromagnets in any dimension. The link overlap results in particular, with peaks at criticality in the kurtosis and the skewness, also have implications for Spin Glasses.