An Exact Solution to a Three Dimensional Ising Model

A high temperature expansion is employed to map some complex anisotropic nonhermitian three dimensional Ising models with algebraic long range interactions into a solvable two dimensional variant. Some solutions are presented. This framework further allows for some very simple general observations. It will be seen that the absence of a “phase interference” effect plays an important role in high dimensional problems. A very forbidding purely algebraic recursive series solution to the three dimensional nearest neighbor Ising model will be given. In the aftermath, the full-blown three dimensional nearest neighbor Ising model is exactly mapped onto a single spin 1/2 particle with nontrivial dynamics.