The bulk, surface and corner free energies of the square lattice Ising model

TL;DR

This paper calculates the bulk, surface, and corner free energies of the anisotropic square lattice Ising model using Kaufman's spinor method, confirming previous conjectures and revealing new insights into their interrelations.

Contribution

It provides the first derivation of the corner free energy $f_c$ for the anisotropic Ising model and analyzes the relationships among all four free energies.

Findings

Agreement with Onsager, McCoy, Wu results for $f_b, f_s, f'_s$

Confirmation of Vernier and Jacobsen's conjecture for $f_c$

Identification of structural links among the free energies

Abstract

We use Kaufman's spinor method to calculate the bulk, surface and corner free energies $f_b, f_s, f_s', f_c$ of the anisotropic square lattice zero-field Ising model for the ordered ferromagnetic case. For $f_b, f_s, f'_s$ our results of course agree with the early work of Onsager, McCoy and Wu. We also find agreement with the conjectures made by Vernier and Jacobsen (VJ) for the isotropic case. We note that the corner free energy $f_c$ depends only on the elliptic modulus $k$ that enters the working, and not on the argument $v$, which means that VJ's conjecture applies for the full anisotropic model. The only aspect of this paper that is new is the actual derivation of $f_c$, but by reporting all four free energies together we can see interesting structures linking them.