Mean-field critical behaviour and ergodicity break in a nonequilibrium one-dimensional RSOS growth model

TL;DR

This study examines a one-dimensional nonequilibrium growth model, revealing a phase transition with mean-field critical behavior and ergodicity breaking, supported by histogram analysis and metastable phase dynamics.

Contribution

It demonstrates the application of off-critical histogram techniques to analyze nonequilibrium phase transitions and uncovers a related model sharing the same critical behavior.

Findings

Phase transition exhibits mean-field critical exponents.

Metastable phase flipping times grow exponentially with system size.

A related model also shows similar phase transition characteristics.

Abstract

We investigate the nonequilibrium roughening transition of a one-dimensional restricted solid-on-solid model by directly sampling the stationary probability density of a suitable order parameter as the surface adsorption rate varies. The shapes of the probability density histograms suggest a typical Ginzburg-Landau scenario for the phase transition of the model, and estimates of the "magnetic" exponent seem to confirm its mean-field critical behaviour. We also found that the flipping times between the metastable phases of the model scale exponentially with the system size, signaling the breaking of ergodicity in the thermodynamic limit. Incidentally, we discovered that a closely related model not considered before also displays a phase transition with the same critical behaviour as the original model. Our results support the usefulness of off-critical histogram techniques in the investigation of nonequilibrium phase transitions. We also briefly discuss in an appendix a good and simple pseudo-random number generator used in our simulations.