# 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.

## Key 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.