Exact solution and interfacial tension of the six-vertex model with anti-periodic boundary conditions

TL;DR

This paper provides an exact solution for the six-vertex model with anti-periodic boundary conditions, deriving the interfacial tension in the anti-ferroelectric phase and discussing related boundary conditions on the XXZ spin chain.

Contribution

It introduces an exact solution for the six-vertex model with anti-periodic boundaries and derives the interfacial tension independently.

Findings

Exact interfacial tension in the anti-ferroelectric phase

Diagonalization of transfer matrix using commuting transfer matrices

Discussion of integrable boundary conditions on the XXZ spin chain

Abstract

We consider the six-vertex model with anti-periodic boundary conditions across a finite strip. The row-to-row transfer matrix is diagonalised by the `commuting transfer matrices' method. {}From the exact solution we obtain an independent derivation of the interfacial tension of the six-vertex model in the anti-ferroelectric phase. The nature of the corresponding integrable boundary condition on the $XXZ$ spin chain is also discussed.