This article is cited in 2 papers

Evidence for a Phase Transition in Three-Dimensional Lattice Models

S. M. Sergeev<sup>ab

a</sup> Max Planck Institute for Mathematics
^b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: It was recently discovered that an eigenvector structure of commutative families of layer-to-layer matrices in three-dimensional lattice models is described by a two-dimensional spin lattice generalizing the notion of one-dimensional spin chains. We conjecture the relations between the two-dimensional spin lattice in the thermodynamic limit and the phase structure of three-dimensional lattice models. We consider two simplest cases: the homogeneous spin lattice related to the Zamolodchikov–Bazhanov–Baxter model and a “chess spin lattice” related to the Stroganov–Mangazeev elliptic solution of the modified tetrahedron equation. Evidence for the phase transition is obtained in the second case.

Keywords: three,dimensional integrable models, Zamolodchikov–Bazhanov–Baxter model.

Received: 18.12.2002

DOI: 10.4213/tmf33

 English version: Theoretical and Mathematical Physics, 2004, 138:3, 310–321

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