Evidence for a~Phase Transition in Three-Dimensional Lattice Models
Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 369-382
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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.
Keywords:
three,dimensional integrable models, Zamolodchikov–Bazhanov–Baxter model.
@article{TMF_2004_138_3_a1,
author = {S. M. Sergeev},
title = {Evidence for {a~Phase} {Transition} in {Three-Dimensional} {Lattice} {Models}},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {369--382},
publisher = {mathdoc},
volume = {138},
number = {3},
year = {2004},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a1/}
}
S. M. Sergeev. Evidence for a~Phase Transition in Three-Dimensional Lattice Models. Teoretičeskaâ i matematičeskaâ fizika, Tome 138 (2004) no. 3, pp. 369-382. http://geodesic.mathdoc.fr/item/TMF_2004_138_3_a1/