Evidence for a Phase Transition in Three-Dimensional Lattice Models |
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Authors: | Sergeev S. M. |
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Affiliation: | (1) Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia;(2) Max-Planck-Institut für Mathematik, Bonn, Germany |
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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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Keywords: | three-dimensional integrable models Zamolodchikov– Bazhanov– Baxter model |
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