Semi-Markov Random Walks and Universality in Ising-like Chains

TL;DR

This paper establishes a correspondence between universal probabilistic properties of one-dimensional Ising-like models and continuous time random walks, offering new insights into the behavior of the ordering coordinate.

Contribution

It introduces a novel correspondence linking Ising-like models with continuous time random walks, providing a new qualitative understanding of their properties.

Findings

Established a one-to-one correspondence between Ising-like models and random walks.

Provided a new qualitative picture of the ordering coordinate's properties.

Highlighted universal probabilistic features shared by both models.

Abstract

We exhibit a one to one correspondence between some universal probabilistic properties of the ordering coordinate of one-dimensional Ising-like models and a class of continuous time random walks. This correspondence provides an new qualitative picture of the properties of the ordering coordinate of the Ising model.