Evidence against a mean field description of short-range spin glasses revealed through thermal boundary conditions

TL;DR

This study uses thermal boundary conditions and population annealing Monte Carlo to investigate the low-temperature phase of short-range spin glasses, providing evidence that supports the droplet picture over mean-field replica symmetry breaking.

Contribution

It introduces a novel numerical approach with thermal boundary conditions to test competing theories of spin glasses, favoring the droplet picture over mean-field models.

Findings

Sample stiffness grows with system size, supporting the droplet picture.

Results are incompatible with mean-field replica symmetry breaking.

Extrapolation aligns with a single pair of pure states description.

Abstract

A theoretical description of the low-temperature phase of short-range spin glasses has remained elusive for decades. In particular, it is unclear if theories that assert a single pair of pure states, or theories that are based infinitely many pure states-such as replica symmetry breaking-best describe realistic short-range systems. To resolve this controversy, the three-dimensional Edwards-Anderson Ising spin glass in thermal boundary conditions is studied numerically using population annealing Monte Carlo. In thermal boundary conditions all eight combinations of periodic vs antiperiodic boundary conditions in the three spatial directions appear in the ensemble with their respective Boltzmann weights, thus minimizing finite-size corrections due to domain walls. From the relative weighting of the eight boundary conditions for each disorder instance a sample stiffness is defined, and its typical value is shown to grow with system size according to a stiffness exponent. An extrapolation to the large-system-size limit is in agreement with a description that supports the droplet picture and other theories that assert a single pair of pure states. The results are, however, incompatible with the mean-field replica symmetry breaking picture, thus highlighting the need to go beyond mean-field descriptions to accurately describe short-range spin-glass systems.