Entropic Effects in the Very Low Temperature Regime of Diluted Ising Spin Glasses with Discrete Couplings

TL;DR

This paper investigates how entropic effects influence the low-temperature behavior of diluted Ising spin glasses, revealing unstable fixed points and emphasizing the importance of entropy considerations for accurate physical modeling.

Contribution

It demonstrates the instability of zero temperature fixed points under temperature perturbations and highlights the necessity of accounting for entropic effects in spin glass models.

Findings

Zero temperature fixed points are unstable with respect to temperature.

Entropic effects are crucial for correct critical behavior.

Spurious fixed points can mislead optimization algorithms.

Abstract

We study link-diluted $\pm J$ Ising spin glass models on the hierarchical lattice and on a three-dimensional lattice close to the percolation threshold. We show that previously computed zero temperature fixed points are unstable with respect to temperature perturbations and do not belong to any critical line in the dilution-temperature plane. We discuss implications of the presence of such spurious unstable fixed points on the use of optimization algorithms, and we show how entropic effects should be taken into account to obtain the right physical behavior and critical points.