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.
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Sergeev, S.M. Evidence for a Phase Transition in Three-Dimensional Lattice Models. Theoretical and Mathematical Physics 138, 310–321 (2004). https://doi.org/10.1023/B:TAMP.0000018448.40360.3d
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DOI: https://doi.org/10.1023/B:TAMP.0000018448.40360.3d