Non-equilibrium phase transition in an exactly solvable driven Ising model with friction

TL;DR

This paper investigates a driven Ising model with friction, revealing a non-equilibrium phase transition that exhibits mean field behavior at high velocities and analyzing the crossover from Ising to mean field regimes through analytical and simulation methods.

Contribution

It provides an exact solution for the driven Ising model with friction at high velocities and compares different spin flip rates, highlighting the non-equilibrium critical behavior.

Findings

Exact solution matches the multiplicative rate.

Different rates lead to different critical temperatures.

Crossover from Ising to mean field behavior analyzed.

Abstract

A driven Ising model with friction due to magnetic correlations has recently been proposed by Kadau et al. (Phys. Rev. Lett. 101, 137205 (2008)). The non-equilibrium phase transition present in this system is investigated in detail using analytical methods as well as Monte Carlo simulations. In the limit of high driving velocities $v$ the model shows mean field behavior due to dimensional reduction and can be solved exactly for various geometries. The simulations are performed with three different single spin flip rates: the common Metropolis and Glauber rates as well as a multiplicative rate. Due to the non-equilibrium nature of the model all rates lead to different critical temperatures at $v>0$, while the exact solution matches the multiplicative rate. Finally, the cross-over from Ising to mean field behavior as function of velocity and system size is analysed in one and two dimensions.