# Numerical construction of the Aizenman-Wehr metastate

## TL;DR

This paper introduces a numerical method to construct the metastate in a 3D Ising spin glass, providing evidence for a dispersed metastate supported on many thermodynamic states, addressing challenges posed by chaotic size dependence.

## Contribution

It presents the first numerical construction of the metastate for a 3D Ising spin glass, leveraging recent rigorous results to analyze its structure.

## Key findings

- Evidence for a dispersed metastate supported on many states
- Numerical construction method for the metastate in disordered systems
- Supports the theoretical prediction of a smooth metastate limit

## Abstract

Chaotic size dependence makes it extremely difficult to take the thermodynamic limit in disordered systems. Instead, the metastate, which is a distribution over thermodynamic states, might have a smooth limit. So far, studies of the metastate have been mostly mathematical. We present a numerical construction of the metastate for the d=3 Ising spin glass. We work in equilibrium, below the critical temperature. Leveraging recent rigorous results, our numerical analysis gives evidence for a "dispersed" metastate, supported on many thermodynamic states.