A Note on Edwards' Hypothesis for Zero-Temperature Ising Dynamics

TL;DR

This paper provides a simple criterion to evaluate Edwards' hypothesis in zero-temperature Ising spin dynamics and demonstrates its invalidity in multiple cases across different dimensions.

Contribution

It introduces a straightforward method to test Edwards' hypothesis and applies it to disprove the hypothesis in various zero-temperature ferromagnetic models.

Findings

Criterion invalidates Edwards' hypothesis in several models

Demonstrates the hypothesis does not hold in higher dimensions

Provides insights into zero-temperature spin dynamics behavior

Abstract

We give a simple criterion for checking the so called Edwards' hypothesis in certain zero-temperature, ferromagnetic spin-flip dynamics and use it to invalidate the hypothesis in various examples in dimension one and higher.