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

2015/10/26 by V. V. Kocharovsky, Kocharovsky, Vitaly V., Kocharovsky, Vladimir V.
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Opinion Dynamics and Social Influence #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1510.07327

openalex publication_date 2015/10/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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