Rates for irreversible Gibbsian Ising models

TL;DR

This paper investigates the rates of irreversible single-spin flip dynamics in Gibbsian Ising models, confirming their existence in 1D and 2D but not in 3D, and explores their behavior at infinite temperature and in conserved dynamics.

Contribution

It provides a comprehensive analysis of irreversible Gibbsian Ising models, including new results on their existence in different dimensions and their behavior at high temperature.

Findings

Gibbsian irreversible Ising models exist in 1D and 2D lattices.

Such models do not exist for the 3D cubic lattice.

At infinite temperature, asymmetric dynamics exhibit specific behaviors.

Abstract

Dynamics under which a system of Ising spins relaxes to a stationary state with Bolzmann-Gibbs measure and which do not fulfil the condition of detailed balance are irreversible and asymmetric. We revisit the problem of the determination of rates yielding such a stationary state for models with single-spin flip dynamics. We add some supplementary material to this study and confirm that Gibbsian irreversible Ising models exist for one and two-dimensional lattices but not for the three-dimensional cubic lattice. We also analyze asymmetric Gibbsian dynamics in the limit of infinite temperature. We finally revisit the case of a linear chain of spins under asymmetric conserved dynamics.