Towards an exact solution for the three-dimensional Ising model: A method of the recurrence equations for partial contractions

We find the exact solutions for the main steps in the analysis of the three-dimensional Ising model. A method is based on a recently found rigorous theory of magnetic phase transitions in a mesoscopic lattice of spins, described as the constrained spin bosons in a Holstein–Primakoff representation....

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Bibliographic Details
Published in:Physics letters. A 2015-10, Vol.379 (39), p.2520-2523
Main Authors: Kocharovsky, Vitaly V., Kocharovsky, Vladimir V.
Format: Article
Language:English
Subjects:
Critical phenomena
Ising model
Mesoscopic system
Phase transition
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Summary:We find the exact solutions for the main steps in the analysis of the three-dimensional Ising model. A method is based on a recently found rigorous theory of magnetic phase transitions in a mesoscopic lattice of spins, described as the constrained spin bosons in a Holstein–Primakoff representation. •Main steps towards exact solution of 3D Ising model are outlined.•Rigorous theory of the constrained spin-boson excitations is formulated.•Novel method of the recurrence equations for partial contractions is proposed.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2015.07.026