Low-temperature behavior of the statistics of the overlap distribution in Ising spin-glass models

TL;DR

This study uses Monte Carlo simulations to analyze the overlap distribution in various spin-glass models at low temperatures, assessing the validity of competing theoretical pictures and exploring new observables.

Contribution

It provides a detailed comparison of overlap distributions across different models and evaluates the effectiveness of new observables in distinguishing theoretical spin-glass phases.

Findings

Larger system sizes are needed to clearly differentiate between RSB and droplet pictures.

The SK model unambiguously exhibits replica symmetry breaking.

Median and typical overlap distributions are not effective discriminators.

Abstract

Using Monte Carlo simulations, we study in detail the overlap distribution for individual samples for several spin-glass models including the infinite-range Sherrington-Kirkpatrick model, short-range Edwards-Anderson models in three and four space dimensions, and one-dimensional long-range models with diluted power-law interactions. We study three long-range models with different powers as follows: the first is approximately equivalent to a short-range model in three dimensions, the second to a short-range model in four dimensions, and the third to a short-range model in the mean-field regime. We study an observable proposed earlier by some of us which aims to distinguish the "replica symmetry breaking" picture of the spin-glass phase from the "droplet picture," finding that larger system sizes would be needed to unambiguously determine which of these pictures describes the low-temperature state of spin glasses best, except for the Sherrington-Kirkpatrick model which is unambiguously described by replica symmetry breaking. Finally, we also study the median integrated overlap probability distribution and a typical overlap distribution, finding that these observables are not particularly helpful in distinguishing the replica symmetry breaking and the droplet pictures.