Blocking and Persistence in the Zero-Temperature Dynamics of Homogeneous and Disordered Ising Models

TL;DR

This paper investigates how disorder and lattice changes influence the zero-temperature dynamics of Ising models, revealing that they can cause blocking and metastability, with some cases showing exponential decay of the persistence probability.

Contribution

It demonstrates that disorder and lattice modifications can induce blocking and metastability in low-dimensional Ising models, with specific examples of exponential decay in persistence.

Findings

Disorder and lattice changes can cause blocking in low-dimensional models.

Persistence probability can decay exponentially to a non-zero value.

Examples show both homogeneous and disordered models exhibit these effects.

Abstract

A ``persistence'' exponent theta has been extensively used to describe the nonequilibrium dynamics of spin systems following a deep quench: for zero-temperature homogeneous Ising models on the d-dimensional cubic lattice, the fraction p(t) of spins not flipped by time t decays to zero like t^[-theta(d)] for low d; for high d, p(t) may decay to p(infinity)>0, because of ``blocking'' (but perhaps still like a power). What are the effects of disorder or changes of lattice? We show that these can quite generally lead to blocking (and convergence to a metastable configuration) even for low d, and then present two examples --- one disordered and one homogeneous --- where p(t) decays exponentially to p(infinity).