Chaos in spin glasses revealed through thermal boundary conditions

TL;DR

This paper investigates the sensitivity of three-dimensional spin glasses to small temperature changes by analyzing free energy crossings under thermal boundary conditions, revealing insights into chaos, domain-wall fractal dimension, and computational hardness.

Contribution

It introduces a numerical approach using thermal boundary conditions to study temperature chaos and domain-wall properties in spin glasses, linking chaos to computational hardness.

Findings

Temperature chaos is evidenced by free energy crossings.

The domain-wall fractal dimension is estimated.

Chaos exponent and its relation to computational hardness are identified.

Abstract

We study the fragility of spin glasses to small temperature perturbations numerically using population annealing Monte Carlo. We apply thermal boundary conditions to a three-dimensional Edwards-Anderson Ising spin glass. In thermal boundary conditions all eight combinations of periodic versus antiperiodic boundary conditions in the three spatial directions are present, each appearing in the ensemble with its respective statistical weight determined by its free energy. We show that temperature chaos is revealed in the statistics of crossings in the free energy for different boundary conditions. By studying the energy difference between boundary conditions at free-energy crossings, we determine the domain-wall fractal dimension. Similarly, by studying the number of crossings, we determine the chaos exponent. Our results also show that computational hardness in spin glasses and the presence of chaos are closely related.