Related papers: Three-coloring statistical model with domain wall …
We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set…
Given an arbitrary choice of two sets of nonzero Boltzmann weights for $n$-color lattice models, we provide explicit algebraic conditions on these Boltzmann weights which guarantee a solution (i.e., a third set of weights) to the…
The trigonometric six-vertex model with domain wall boundary conditions and one partially reflecting end on a lattice of size $2n\times m$, $m\leq n$, is considered. The partition function is computed using the Izergin-Korepin method,…
Critical site percolation on the triangular lattice is described by the Yang-Baxter solvable dilute $A_2^{(2)}$ loop model with crossing parameter specialized to $\lambda=\frac\pi3$, corresponding to the contractible loop fugacity…
We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the…
I consider the partition function of the inhomogeneous 6-vertex model defined on the $n$ by $n$ square lattice. This function depends on 2n spectral parameters $x_i$ and $y_i$ attached to the horizontal and vertical lines respectively. In…
We consider the problem of calculation of correlation functions in the six-vertex model with domain wall boundary conditions. To this aim, we formulate the model as a scalar product of off-shell Bethe states, and, by applying the quantum…
We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the "darkness formation probability" are calculated in the thermodynamical…
We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…
The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded…
The N-particle partition function of a one-dimensional $\delta$-function bose gas is calculated explicitly using only the periodic boundary condition (the Bethe ansatz equation). The N-particles cluster integrals are shown to be the same as…
We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…
We compute the partition function of the $q$-states Potts model on a random planar lattice with $p\leq q$ allowed, equally weighted colours on a connected boundary. To this end, we employ its matrix model representation in the planar limit,…
A boundary one point function related to the boundary spontaneous polarization, which is different from the ones considered in the past, is studied for the six vertex model on a 2N \times N lattice with domain wall boundary condition and…
We consider a rational six vertex model on a rectangular lattice with boundary conditions that generalize the usual domain wall type. We find that the partition function of the inhomogeneous version of this model is given by a modified…
We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang-Baxter algebra. The main deviation from the standard approach consists in a half infinite 'Sklyanin lattice' made of the eigenvalues of…
In the present paper the three state Potts model with competing binary interactions (with couplings $J$ and $J_p$) on the second order Bethe lattice is considered. The recurrent equations for the partition functions are derived. When…
We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz…
In this paper, we introduce a class of colored stochastic vertex models with U-turn right boundary. The vertex weights in the models satisfy the Yang-Baxter equations and the reflection equation. Based on these equations, we derive…
In this paper we continue the study of the three-layer Zamolodchikov model started in our previous works. We analyse numerically the solutions to the Bethe ansatz equations. We consider two regimes I and II which differ by the signs of the…