Numerical Simulations of Finite Dimensional Spin Glasses Show a Mean Field like Behavior

TL;DR

Numerical simulations of finite dimensional spin glasses reveal mean field-like behavior, including signatures such as the Parisi solution, Binder cumulant, and non self-averaging properties, enhancing understanding of their complex phase structure.

Contribution

This study demonstrates that finite dimensional spin glasses exhibit mean field characteristics, aligning with the Parisi solution, through comprehensive numerical analysis.

Findings

Finite dimensional spin glasses show mean field signatures.

The Parisi solution describes the behavior of these systems.

Correlation functions and spatial observables support mean field behavior.

Abstract

I discuss results from numerical simulations of finite dimensional spin glass models, and show that they show all signatures of a mean field like behavior, basically coinciding with the one of the Parisi solution. I discuss the Binder cumulant, the probability distribution of the order parameter, the non self-averaging behavior. The determination of correlation function and of spatially blocked observables quantities helps in qualifying the behavior of the system.