Towards integrable structure in 3d Ising model

JOURNAL OF GEOMETRY AND PHYSICS

卷:148

Article

Talalaev, Dmitry, V^1,2,3 

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia

[2] NRC Kurchatov Inst, Inst Theoret & Expt Phys, 25 Bolshaya Cheremushkinskaya Str, Moscow 117218, Russia

[3] PG Demidov Yaroslavl State Univ, Ctr Integrable Syst, 14 Sovetskaya Str, Yaroslavl 150003, Russia

关键词: Ising model;    Zamolodchikov tetrahedron equation;    Gray code;   

DOI  :  10.1016/j.geomphys.2019.103545

来源: Elsevier

【 摘 要 】

In this paper, we proceed to the study of tetrahedral symmetry in the 3D Ising model, which is considered as the first forerunner of integrability. The weight matrix of the model on a regular cubic lattice satisfying the twisted tetrahedron equation (TTE) is constructed. The latter is a modification of the Zamolodchikov tetrahedron equation, which appeared in integrable 3D statistical models. The method is based on the theory of the n-simplicial complex and the original recursion procedure on the space of n-simplex solutions. This recursion deserves its own investigation. Surprisingly, the weight matrix has some properties inherent for the hypercube combinatorics and coding theory. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free