A single-variable integral representation of the Ising model partition function

A new method to transform a partition function of the Ising model to a single-variable integral is presented. It allows to account for an interaction with next nearest neighbours and with an external magnetic field as well. The method is valid for any dimension or type of lattice. Using this approach, a mapping of the Ising model onto a symmetric function problem is obtained and demonstrated in the 1d case.