Relation between Yang-Baxter and Pair Propagation Equations in 16-Vertex Models

We study a relation between two integrability conditions, namely the Yang-Baxter and the pair propagation equations, in 2D lattice models. While the two are equivalent in the 8-vertex models, discrepancies appear in the 16-vertex models. As explicit examples, we find the exactly solvable 16-vertex models which do not satisfy the Yang-Baxter equations.Comment: 11 pages, TEZU-F-059 and EWHA-TH-00

The Structure of the Bazhanov-Baxter Model and a New Solution of the Tetrahedron Equation

We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state integrable model. There are two essential points, i) the cubic symmetries, and ii) the spherical trigonometry parametrization, to understand the structure of this model. We propose two approaches to find a candidate as a solution of the tetrahedron equation, and we find a new solution.Comment: 23 pages, Late

Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

In order to determine the Wigner function uniquely, we introduce a new condition which ensures that the Wigner function has correct marginal distributions along tilted lines. For a system in $N$ dimensional Hilbert space, whose "phase space" is a lattice with $N^2$ sites, we get different results depending on whether $N$ is odd or even. Under the new condition, the Wigner function is determined if $N$ is an odd number, but it does not exist if $N$ is even.Comment: 18 page

Wigner Functions on a Lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE