What Does It Take to Solve the 3D Ising Model? Minimal Necessary Conditions for a Valid Solution.

An exact solution of the Ising model on the simple cubic lattice is one of the long-standing open problems in rigorous statistical mechanics. Indeed, it is generally believed that settling it would constitute a methodological breakthrough, fomenting great prospects for further application, similarly to what happened when Lars Onsager solved the two-dimensional model eighty years ago. Hence, there have been many attempts to find analytic expressions for the exact partition function , but all such attempts have failed due to unavoidable conceptual or mathematical obstructions.