Exact solution of a general two-dimensional Ising model: The partition function

The exact partition function per spin is obtained for a two-dimensional generalization of the Ising model. This general model consists of a unitary cell that is repeated throughout the system. The unitary cell is made up of spins in t columns and q rows with arbitrary energies between them. The exact result is given in terms of certain Ψ quantities (see section 2), which can be determined for particular cases.

It is always possible to transform the unit cell in order to obtain a desired given model. Thus, the results for several known models are recovered, e.g., the Utiyama and the hexagonal (with three different interaction parameters) models. Furthermore, explicit results are presented for other models hitherto not reported in the literature, as are the general hexagonal (with six different interaction parameters), the general triangular model (with six different interaction parameters) and the tetragonal-triangular (with seven different interaction parameters) models.