Ising model as Wilson-Majorana fermions

Abstract

We show the equivalence of the 2D Ising model to standard free Euclidean lattice fermions of the Wilson Majorana type. The equality of the loop representations for the partition functions of both systems is established exactly for finite lattices with well-defined boundary conditions. The honeycomb lattice is particularly simple in this context and therefore discussed first and only then followed by the more familiar square lattice case.