Single-spin-flip dynamics of the Ising chain

TL;DR

This paper explores a generalized class of single-spin-flip dynamics for the ferromagnetic Ising chain, analyzing their properties at various temperatures and identifying special cases within the parameter space.

Contribution

It introduces a two-parameter extension of Glauber dynamics that includes non-linearity and irreversibility, while maintaining the Boltzmann-Gibbs stationary measure.

Findings

Stationary state remains the Boltzmann-Gibbs distribution.

Dynamics exhibit distinct behaviors at special parameter lines and points.

Analysis covers both infinite and finite temperature regimes.

Abstract

We consider the most general single-spin-flip dynamics for the ferromagnetic Ising chain with nearest-neighbour influence and spin reversal symmetry. This dynamics is a two-parameter extension of Glauber dynamics corresponding respectively to non-linearity and irreversibility. The associated stationary state measure is given by the usual Boltzmann-Gibbs distribution for the ferromagnetic Hamiltonian of the chain. We study the properties of this dynamics both at infinite and at finite temperature, all over its parameter space, with particular emphasis on special lines and points.