First-order phase transitions in one-dimensional steady states

TL;DR

This paper investigates the phase transitions in a one-dimensional two-species exclusion model, revealing complex shock patterns, non-convex free energy, and novel dynamical critical exponents through Monte Carlo simulations and spectral analysis.

Contribution

It demonstrates the failure of mean-field theory for the phase diagram and uncovers unexpected shock patterns and critical exponents in the model.

Findings

Mean-field theory does not accurately predict the phase diagram.

Shock patterns explain density profiles on the first-order transition line.

Massless excitations with dynamical critical exponent z=2 are observed at the transition.

Abstract

The steady states of the two-species (positive and negative particles) asymmetric exclusion model of Evans, Foster, Godreche and Mukamel are studied using Monte Carlo simulations. We show that mean-field theory does not give the correct phase diagram. On the first-order phase transition line which separates the CP-symmetric phase from the broken phase, the density profiles can be understood through an unexpected pattern of shocks. In the broken phase the free energy functional is not a convex function but looks like a standard Ginzburg-Landau picture. If a symmetry breaking term is introduced in the boundaries the Ginzburg-Landau picture remains and one obtains spinodal points. The spectrum of the hamiltonian associated with the master equation was studied using numerical diagonalization. There are massless excitations on the first-order phase transition line with a dynamical critical exponent z=2 as expected from the existence of shocks and at the spinodal points where we find $z=1$. It is for the first time that this value which characterizes conformal invariant equilibrium problems appears in stochastic processes.