Bulk, surface and corner free energies of the anisotropic triangular Ising model: series expansions and critical behaviour

Abstract: We consider the anisotropic Ising model on the triangular lattice with finite boundaries, and use Kaufman's spinor method to calculate low-temperature series expansions for the partition function to high order. From these we can obtain 108-term series expansions for the bulk, surface and corner free energies. We extrapolate these to all terms and thereby conjecture the exact results for each. Our results agree with the exactly known bulk free energy. For the isotropic case, they also agree with Vernier and Jacobsen's conjecture for the $60<sup>{\circ}$ corners, and with Cardy and Peschel's conformal invariance predictions for the dominant behaviour at criticality.