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We have derived exact expressions for the domain wall free energy along thethree high-symmetry directions of a triangular lattice with anisotropicnearest-neighbor interactions. The triangular lattice undergoes anorderdisorder 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 thenearest-neighbor interaction energies, and e1+ e2> 0, e2+ e3> 0, e3+ e1> 0.Finally, we have derived expressions for the thermally induced meandering ofthe domain walls at temperatures below the phase transition temperature. Weshow how these expressions can be used to extract the interaction energies oftwo-dimensional systems with a triangular lattice.

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