The entropy of the six-vertex model with variety of different boundary conditions

TL;DR

This paper investigates how boundary conditions affect the entropy of the six-vertex model, showing that many boundary types lead to the same free-energy in the thermodynamic limit, with some fixed boundaries causing continuous entropy variation.

Contribution

It demonstrates the equivalence of free-energy for various boundary conditions in the thermodynamic limit and identifies fixed boundaries that alter entropy continuously.

Findings

Periodic, anti-periodic, and mixed boundaries yield the same free-energy asymptotically.

Certain fixed boundary conditions cause entropy to vary continuously from zero to the periodic case.

Physical quantities remain unchanged at the isotropic point under singular toroidal boundary.

Abstract

We study the dependence of entropy [per lattice site] of six-vertex model on boundary conditions. We start with lattices of finite size and then proceed to thermodynamic limit. We argue that the six-vertex model with periodic, anti-periodic and mixed boundary conditions produce the same free-energy in the thermodynamic limit. We have found fixed boundary conditions such that the entropy varies continously from zero to its value for periodic boundary condition. We have also shown that the physical quantities of the six-vertex model at the isotropic point does not change in the case of singular toroidal boundary.