Metastability in zero-temperature dynamics: Statistics of attractors

TL;DR

This paper investigates the statistical properties and spatial structures of metastable attractors in zero-temperature Ising models, providing new exact results for two-dimensional lattices and comparing them with theoretical ensembles.

Contribution

It offers novel insights into the structure and statistics of metastable states in zero-temperature Ising dynamics, including original results for square and honeycomb lattices.

Findings

Exact results for one-dimensional models

New characterization of attractors in 2D lattices

Comparison with uniform a priori ensembles

Abstract

The zero-temperature dynamics of simple models such as Ising ferromagnets provides, as an alternative to the mean-field situation, interesting examples of dynamical systems with many attractors (absorbing configurations, blocked configurations, zero-temperature metastable states). After a brief review of metastability in the mean-field ferromagnet and of the droplet picture, we focus our attention onto zero-temperature single-spin-flip dynamics of ferromagnetic Ising models. The situations leading to metastability are characterized. The statistics and the spatial structure of the attractors thus obtained are investigated, and put in perspective with uniform a priori ensembles. We review the vast amount of exact results available in one dimension, and present original results on the square and honeycomb lattices.