Evidence for a phase transition in three-dimensional lattice models

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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
Original languageEnglish
Pages (from-to)310-321
Number of pages12
JournalTheoretical and Mathematical Physics
Issue number3
Publication statusPublished - Mar 2004
Externally publishedYes


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