Free energy of domain walls and order-disorder transition in a triangular lattice with anisotropic nearest-neighbor interactions

TL;DR

This paper derives exact formulas for domain wall free energy and analyzes the order-disorder transition in a triangular lattice with anisotropic interactions, providing tools to determine interaction energies from thermal domain wall behavior.

Contribution

It presents the first exact expressions for domain wall free energy in a triangular lattice with anisotropic interactions and relates these to the phase transition and domain wall meandering.

Findings

Exact domain wall free energy expressions along high-symmetry directions.

A phase transition temperature formula based on interaction energies.

Expressions for thermally induced domain wall meandering.

Abstract

We have derived exact expressions for the domain wall free energy along the three high-symmetry directions of a triangular lattice with anisotropic nearest-neighbor interactions. The triangular lattice undergoes an orderdisorder phase transition at a temperature Tc given by exp(-(e1+e2)/2kTc)+ exp(-(e2+e3)/2kTc)+ exp(-(e3+e1)/2kTc)= 1, where e1, e2, e3 are the nearest-neighbor interaction energies, and e1+ e2> 0, e2+ e3> 0, e3+ e1> 0. Finally, we have derived expressions for the thermally induced meandering of the domain walls at temperatures below the phase transition temperature. We show how these expressions can be used to extract the interaction energies of two-dimensional systems with a triangular lattice.