Evidence for a phase transition in three-dimensional lattice models

Sergey Sergeev

Research output: Contribution to journalArticle

1 Citation (Scopus)

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
Original languageEnglish
Pages (from-to)310-321
Number of pages12
JournalTheoretical and Mathematical Physics
Volume138
Issue number3
DOIs
Publication statusPublished - Mar 2004
Externally publishedYes

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Lattice Model
Phase Transition
Three-dimensional
Spin Chains
Triangular pyramid
Thermodynamic Limit
Eigenvector
tetrahedrons
Evidence
eigenvectors
thermodynamics
matrices
Model

Cite this

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Evidence for a phase transition in three-dimensional lattice models. / Sergeev, Sergey.

In: Theoretical and Mathematical Physics, Vol. 138, No. 3, 03.2004, p. 310-321.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Evidence for a phase transition in three-dimensional lattice models

AU - Sergeev, Sergey

PY - 2004/3

Y1 - 2004/3

N2 - 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

AB - 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

KW - three-dimensional integrable models

KW - Zamolodchikov-Bazhanov-Baxter model

U2 - 10.1023/B:TAMP.0000018448.40360.3d

DO - 10.1023/B:TAMP.0000018448.40360.3d

M3 - Article

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JO - Theoretical and Mathematical Physics(Russian Federation)

JF - Theoretical and Mathematical Physics(Russian Federation)

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