An integrable 3D lattice model with positive Boltzmann weights

Abstract

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 generalisation 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 solvable 3D lattice model with non-negative Boltzmann weights.

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References in corpus (3)

• On the Yang-Baxter equation for the six-vertex model
• Quantum geometry of 3-dimensional lattices
• Classical integrable field theories in discrete 2+1 dimensional space-time

Cited by in corpus (14)

• On the Yang-Baxter equation for the six-vertex model
• Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
• Q-operators in the six-vertex model
• Construction of $R$-matrices for symmetric tensor representations related to $U_q(\widehat{s{l}_n})$
• Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
• Cohomologies of $n$-simplex relations
• Tetrahedron equation and quantum R matrices for $q$-oscillator representations of $U_q(A_{2n}^{(2)}),U_q(C_n^{(1)})$ and $U_q(D_{n+1}^{(2)})$
• Solving the Yang-Baxter, tetrahedron and higher simplex equations using Clifford algebras
• The Yang-Baxter relation and gauge invariance
• Stochasticization of Solutions to the Yang-Baxter Equation
• An Ising-type formulation of the six-vertex model
• Solution of tetrahedron equation and cluster algebras
• Tetrahedron equation and Schur functions
• Majorana fermions solve the tetrahedron equations as well as higher simplex equations