Bethe Ansatz in the Bernoulli matching model of random sequence alignment.

Bethe Ansatz for the FPL 2 model

An exact solution of the model of fully packed loops of two colors on a square lattice has recently been proposed by Dei Cont and Nienhuis using the coordinate Bethe Ansatz approach. We point out here a simpler alternative, in which the transfer matrix is directly identified as a product of R-matrices; this allows to apply the (nested) algebraic Bethe Ansatz, which leads to the same Bethe equat...

The Exact Solution of an Octagonal Rectangle Triangle Random Tiling

We present a detailed calculation of the recently published exact solution of a random tiling model possessing an eight-fold symmetric phase. The solution is obtained using Bethe Ansatz and provides closed expressions for the entropy and phason elastic constants. Qualitatively, this model has the same features as the square-triangle random tiling model. We use the method of P. Kalugin, who solv...

Heisenberg Model, Bethe Ansatz, and Random Walks

Multiple Orthogonal Polynomials and a Counterexample to Gaudin Bethe Ansatz Conjecture

Jacobi polynomials are polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two sl2 irreducible modules. We study sequences of r polynomials whose zeros form the unique solution of the Bethe Ansatz equation associated with two highest weight slr+1 irreducible modules, with the restriction that the highest weight of one of the modules is a multiple of the...

Bethe ansatz solution of triangular trimers on the triangular lattice.

Recently, a model consisting of triangular trimers covering the triangular lattice was introduced and its exact free energy given. In this paper we present the complete calculation leading to this exact result. The solution involves a coordinate Bethe ansatz with two kinds of particles. It is similar to that of the square-triangle random tiling model by Widom and Kalugin. The connection of the ...