Related papers: On the integrability of the square-triangle random…
We introduce a class of new integrable lattice models labeled by a pair of positive integers N and r. The integrable model is obtained from the Gauge/YBE correspondence, which states the equivalence of the 4d N=1 S^1 \times S^3/Z_r index of…
We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…
The work contains a detailed study of the scaling limit of a certain critical, integrable inhomogeneous six-vertex model subject to twisted boundary conditions. It is based on a numerical analysis of the Bethe ansatz equations as well as…
The fully-packed loop model of closed paths covering the honeycomb lattice is studied through its identification with the $sl_q(3)$ integrable lattice model. Some known results from the Bethe ansatz solution of this model are reviewed. The…
We consider the problem of counting the number of 3-colourings of the edges (bonds) of the 4-8 lattice and the 3-12 lattice. These lattices are Archimedean with coordination number 3, and can be regarded as decorated versions of the square…
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex…
We develop a unified formulation of the quantum inverse scattering method for lattice vertex models associated to the non-exceptional $A^{(2)}_{2r}$, $A^{(2)}_{2r-1}$, $B^{(1)}_r$, $C^{(1)}_r$, $D^{(1)}_{r+1}$ and $D^{(2)}_{r+1}$ Lie…
We investigate various aspects of the integrability of the vertex models associated to the $D_n^2$ affine Lie algebra with open boundaries. We first study the solutions of the corresponding reflection equation compatible with the minimal…
Lie algebra valued equations translating the integrability of a general two-dimensional Wess-Zumino-Witten model are given. We found simple solutions to these equations and identified three types of new integrable non-linear sigma models.…
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…
The solvable $sl(n)$-chiral Potts model can be interpreted as a three-dimensional lattice model with local interactions. To within a minor modification of the boundary conditions it is an Ising type model on the body centered cubic lattice…
We show that the solutions of the Yang--Baxter equation invariant under the action of the Yangian $Y(sl_2)$ lead to inhomogenous vertex models. Starting from a four dimensional representation of $Y(sl_2)$ we obtain an integrable family of…
In this paper we formulate a new N-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice. This model can be also reformulated as a vertex type model. Weight functions of…
We propose an approach to construct three-dimensional lattice models using line defects in state integral models on shaped triangulations of 3-manifolds. The Boltzmann weights for these models satisfy a variant of the tetrahedron equation,…
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked surfaces. Based on this, we establish a bijection between tagged permissible curves and certain…
Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear…
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…
We introduce triples of associative algebras as a tool for building solutions to the Yang-Baxter equation. It turns out that the class of R-matrices thus obtained is related to a Hecke-like condition, which is formulated for associative…
We show how to compute the exact partition function for lattice statistical-mechanical models whose Boltzmann weights obey a special "crossing" symmetry. The crossing symmetry equates partition functions on different trivalent graphs,…
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…