Diffusive Thermal Dynamics for the Ising Ferromagnet

TL;DR

This paper presents a diffusive thermal dynamics model for the Ising ferromagnet, where a walker-based process drives the system to a non-canonical stationary state, revealing a shifted phase transition and dependence on walker density.

Contribution

It introduces a novel diffusive thermal dynamics for the Ising model that results in non-trivial stationary states and modifies the phase transition point compared to canonical equilibrium.

Findings

Stationary state differs from Boltzmann equilibrium.

Phase transition occurs at higher temperature than canonical.

Increasing walker density reduces differences from equilibrium.

Abstract

We introduce a thermal dynamics for the Ising ferromagnet where the energy variations occurring within the system exhibit a diffusive character typical of thermalizing agents such as e.g. localized excitations. Time evolution is provided by a walker hopping across the sites of the underlying lattice according to local probabilities depending on the usual Boltzmann weight at a given temperature. Despite the canonical hopping probabilities the walker drives the system to a stationary state which is not reducible to the canonical equilibrium state in a trivial way. The system still exhibits a magnetic phase transition occurring at a finite value of the temperature larger than the canonical one. The dependence of the model on the density of walkers realizing the dynamics is also discussed. Interestingly the differences between the stationary state and the Boltzmann equilibrium state decrease with increasing number of walkers.