A Novel Approach to Ising Problems

In 2000 Istrail suggested that calculating the partition function of non-planar Ising models is an NP-complete problem, implying that these problems are intractable and thus essentially unsolvable. In this note we discuss the validity of this suggestion and introduce the idea of gauging on an exact equation. We illustrate how this method works by applying it to two non-planar Ising models, namely the 2D model with nearest and weak next nearest neighbor interactions and the anisotropic 3D model