Interface localization in the 2D Ising model with a driven line

TL;DR

This paper investigates how a one-dimensional driven field influences the behavior and localization of interfaces in a 2D Ising model, revealing multiple phases with different interface fluctuations and symmetry properties.

Contribution

It provides an exact solution for the phase diagram of a driven 2D Ising model with a central ring, showing novel interface localization phenomena and symmetry breaking effects.

Findings

Identifies phases with symmetric and asymmetric interface fluctuations.

Discovers a phase where the interface is localized in the bulk, either above or below the central ring.

Shows stronger symmetry breaking than in equilibrium with a repulsive potential.

Abstract

We study the effect of a one-dimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the two-dimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is `stronger' than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solid-on-solid model.