Free fermion approximation for the Ising model with further-neighbor interactions on a triangular lattice

Abstract

The free fermion solution/approximation for the Ising model on a triangular lattice with further-neighbor interactions is derived, using Vdovichenko's method. For isotropic first- and second-neighbor interactionsK,L⩾0, the approximation is a strict lower bound for the partition sum. We have also obtained the approximate critical surface, where the critical behavior is Ising-like, and the exact zero-temperature phase diagram when the interactions are isotropic. A recent extension of the method of Vdovichenko due to Calheiroset al. makes it easy to give the surface free energy and the equilibrium crystal shape as well, in the ferromagnetic regime and for a regime where the phase is ordered in layers.