Study of a microcanonical algorithm on the $\pm J$ spin glass model in d=3

TL;DR

This study compares microcanonical and canonical Monte Carlo algorithms on the 3D $ ext{±}J$ spin glass model, revealing ensemble-dependent differences that diminish with larger system sizes and confirming Guerra relations at large volumes.

Contribution

It provides a comparative analysis of microcanonical and canonical algorithms on the 3D $ ext{±}J$ spin glass model, highlighting differences and confirming theoretical relations.

Findings

Differences between ensembles decrease with larger lattice sizes.

Microcanonical thermalization times are longer than canonical.

Guerra relations are satisfied at large system sizes.

Abstract

We consider a microcanonical local algorithm to be applied on the $\pm J$ spin glass model. We have compared the results coming from a microcanonical Monte Carlo simulation with those from a canonical one: Thermalization times, spin glass susceptibilities and Binder parameters. For a fixed lattice size we found different results between the two thermodynamic ensembles, which tend to vanish at bigger volumes. Moreover, microcanonical thermalization times are longer than the canonical ones. Finally we have checked that one of the Guerra relations is satisfied with good precision for the two largest lattices.