Interacting Domain Walls and the Five-Vertex Model

TL;DR

This paper analyzes an interacting domain wall model derived from the triangular lattice antiferromagnetic Ising model, revealing its phase diagram with commensurate and incommensurate phases, and characterizing the critical properties using Bethe Ansatz and conformal field theory.

Contribution

It provides an exact solution of the model's phase diagram and critical properties, including the Gaussian coupling constant, using Bethe Ansatz and finite size scaling.

Findings

Phase diagram with commensurate and incommensurate phases

Critical incommensurate phase described by Gaussian fixed point

Gaussian coupling varies smoothly within the incommensurate region

Abstract

We investigate the thermodynamic and critical properties of an interacting domain wall model which is derived from the triangular lattice antiferromagnetic Ising model with the anisotropic nearest and next nearest neighbor interactions. The model is equivalent to the general five--vertex model. Diagonalizing the transfer matrix exactly by the Bethe Ansatz method, we obtain the phase diagram displaying the commensurate and incommensurate (IC) phases separated by the Pokrovsky--Talapov transitions. The phase diagram exhibits commensurate phases where the domain wall density $q$ is locked at the values of $0$, $1/2$ and $1$. The IC phase is a critical state described by the Gaussian fixed point. The effective Gaussian coupling constant is obtained analytically and numerically for the IC phase using the finite size scaling predictions of the conformal field theory. It takes the value $1/2$ in the non-interacting limit and also at the boundaries of $q=0$ or $1$ phase and the value $2$ at the boundary of $q=1/2$ phase, while it varies smoothly throughout the IC region. (TO APPEAR IN PHY. REV. E)