Phase transitions in interacting domain-wall model

TL;DR

This paper studies phase transitions in an interacting domain-wall model derived from a triangular-lattice antiferromagnetic Ising system, revealing KT and first-order transitions and characterizing the critical phases.

Contribution

It provides a detailed analysis of the phase diagram, critical behavior, and transition types in the domain-wall model using Monte Carlo and transfer-matrix methods.

Findings

KT transition separates commensurate and incommensurate phases.

Strong attraction induces a first-order transition from q=0 to incommensurate phase.

Incommensurate phase exhibits Gaussian universality class.

Abstract

We investigate the interacting domain-wall model derived from the triangular-lattice antiferromagnetic Ising model with two next-nearest-neighbor interactions. The system has commensurate phases with a domain-wall density $q=2/3$ as well as that of $q=0$ when the interaction is repulsive. The $q=2/3$ commensurate phase is separated from the incommensurate phase through the Kosterlitz--Thouless~(KT) transition. The critical interaction strength and the nature of the KT phase transition are studied by the Monte Carlo simulations and numerical transfer-matrix calculations. For strongly attractive interaction, the system undergoes a first-order phase transition from the $q=0$ commensurate phase to the incommensurate phase with $q\neq 0$. The incommensurate phase is a critical phase which is in the Gaussian model universality class. The effective Gaussian coupling constant is calculated as a function of interaction parameters from the finite-size scaling of the transfer matrix spectra .