TY - JOUR

T1 - An integrable 3D lattice model with positive Boltzmann weights

AU - Mangazeev, Vladimir V.

AU - Bazhanov, Vladimir V.

AU - Sergeev, Sergey

PY - 2013/11/22

Y1 - 2013/11/22

N2 - In this paper we construct a three-dimensional (3D) solvable lattice model with
non-negative Boltzmann weights. The spin variables in the model are assigned
to edges of the 3D cubic lattice and run over an infinite number of discrete
states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D
generalization of the Yang–Baxter equation. The weights depend on a free
parameter 0 < q < 1 and three continuous field variables. The layer-to-layer
transfer matrices of the model form a two-parameter commutative family. This
is the first example of a non-trivial solvable 3D lattice model with non-negative
Boltzmann weights.

AB - In this paper we construct a three-dimensional (3D) solvable lattice model with
non-negative Boltzmann weights. The spin variables in the model are assigned
to edges of the 3D cubic lattice and run over an infinite number of discrete
states. The Boltzmann weights satisfy the tetrahedron equation, which is a 3D
generalization of the Yang–Baxter equation. The weights depend on a free
parameter 0 < q < 1 and three continuous field variables. The layer-to-layer
transfer matrices of the model form a two-parameter commutative family. This
is the first example of a non-trivial solvable 3D lattice model with non-negative
Boltzmann weights.

KW - (blank)

U2 - 10.1088/1751-8113/46/46/465206

DO - 10.1088/1751-8113/46/46/465206

M3 - Article

SN - 1751-8113

VL - 46

SP - 1

EP - 16

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

IS - 46

ER -