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

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 order-disorder phase transition at a temperature Tc given by e-(ϵ1+ϵ2)/2kTc+e-(ϵ2+ϵ3)/2kTc+e-(ϵ3+ϵ1)/2kTc=1, where ϵ1, ϵ2, ϵ3 are the nearest-neighbor interaction energies, and ϵ1+ϵ2>0, ϵ2+ϵ3>0, ϵ3+ϵ1>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.