Exact general solution to the three-dimensional Ising model and a self-consistency equation for the nearest-neighbors' correlations

Abstract

We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial contractions of creation and annihilation operators for constrained spin bosons in a Holstein-Primakoff representation. In particular, we calculate analytically the total irreducible self-energy, the order parameter, the correlation functions, and the joined occupation probabilities of spin bosons. The developed regular microscopic quantum-field-theory method has a potential for a full solution of a long-standing and still open problem of 3D critical phenomena.