Related papers: Functional Relations in Solvable Lattice Models II

We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…

The family of $A^{(1)}_2$ models on the square lattice includes a dilute loop model, a $15$-vertex model and, at roots of unity, a family of RSOS models. The fused transfer matrices of the general loop and vertex models are shown to satisfy…

The functional relations of the transfer matrices of fusion hierachies for six- and eight-vertex models with open boundary conditions have been presented in this paper. We have shown the su($2$) fusion rule for the models with more general…

The $N$-state chiral Potts model in lattice statistical mechanics can be obtained as a ``descendant'' of the six-vertex model, via an intermediate ``$Q$'' or ``$\tau_2 (t_q)$'' model. Here we generalize this to obtain a column-inhomogeneous…

The fusion hierarchy, $T$-system and $Y$-system of functional equations are the key to integrability for 2d lattice models. We derive these equations for the generic dilute $A_2^{(2)}$ loop models. The fused transfer matrices are associated…

The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…

In this paper, we consider the unitary critical restricted-solid-on-solid (RSOS) lattice $\mathcal{M}(5,6)$ model with integrable boundary conditions. We introduce its commuting double row transfer matrix satisfying the universal functional…

We study linear relations among correlation functions on a lattice obtained from integration-by-parts identities. We use the framework of twisted cocycles and determine for a scalar theory a basis of correlation functions, in which all…

This article is concerned with a mathematical tool, the Associated Transfer Matrix T, which proves useful in the study of a wide class of physical problems involving multilayer heterostructures. General properties of linear, second order…

We give an overview of the theory of functional relations for zeta-functions of root systems, and show some new results on functional relations involving zeta-functions of root systems of types $B_r$, $D_r$, $A_3$ and $C_2$. To show those…

Multisite interaction spin-S models in an external magnetic field are studied recursively on the Bethe-like lattices. The transfer-matrix method is extended to calculate exactly the two-spin correlation functions. The exact expressions for…

An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is…

We find linear (as well as quadratic) relations in a very large class of T-functions. The relations may be used in analysis of T-function-based stream ciphers.

An equivalence between generalised restricted solid-on-solid (RSOS) models, associated with sets of graphs, and multi-colour loop models is established. As an application we consider solvable loop models and in this way obtain new solvable…

RSOS models based on the Lie algebras $B_m$, $C_m$ and $D_m$ are derived from the braiding of conformal field theory. This gives the first systematic derivation of these models earlier described by Jimbo et al. The general two field…

We introduce and solvev a special family of integrable interacting vertex models that generalizes the well known six-vertex model. In addition to the usual nearest-neighbor interactions among the vertices, there exist extra hard-core…

Based on the vertex-face correspondence, we give an algebraic analysis formulation of correlation functions of the $k\times k$ fusion eight-vertex model in terms of the corresponding fusion SOS model. Here $k\in Z_{>0}$. A general formula…

We briefly describe what tau-functions in integrable systems are. We then define a collection of tau-functions given as matrix elements for the action of $\widehat{GL_2}$ on two-component Fermionic Fock space. These tau-functions are…

We construct a family of solvable lattice models whose partition functions include $p$-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating…

Eigenvalues of the commuting family of transfer matrices are expected to obey the $T$-system, a set of functional relation, proposed recently. Here we obtain the solution to the $T$-system for $C^{(1)}_2$ vertex models. They are compatible…