Spontaneous Breaking of Translational Invariance in One-Dimensional Stationary States on a Ring

TL;DR

This paper investigates a one-dimensional particle model on a ring, revealing three distinct phases including a spontaneously translational symmetry-breaking phase, through simulations and analysis.

Contribution

It introduces a new model with asymmetric particle diffusion and swaps, demonstrating phase behavior and spontaneous symmetry breaking in one-dimensional stationary states.

Findings

Identification of three phases: pure, mixed, and disordered.

Spontaneous breaking of translational invariance in the pure phase.

Existence of a non-zero current in the mixed phase.

Abstract

We consider a model in which positive and negative particles diffuse in an asymmetric, CP-invariant way on a ring. The positive particles hop clockwise, the negative counterclockwise and oppositely-charged adjacent particles may swap positions. Monte-Carlo simulations and analytic calculations suggest that the model has three phases; a "pure" phase in which one has three pinned blocks of only positive, negative particles and vacancies, and in which translational invariance is spontaneously broken, a "mixed" phase with a non-vanishing current in which the three blocks are positive, negative and neutral, and a disordered phase without blocks.