Related papers: New Developments in the Eight Vertex Model II. Cha…

We construct a $Q$-matrix for the eight-vertex model at roots of unity for crossing parameter $\eta=2mK/L$ with odd $L$, a case for which the existing constructions do not work. The new $Q$-matrix $\Q$ depends as usual on the spectral…

We extend our studies of the TQ equation introduced by Baxter in his 1972 solution of the 8 vertex model with parameter $\eta$ given by $2L\eta=2m_1K+im_2K'$ from $m_2=0$ to the more general case of complex $\eta.$ We find that there are…

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even…

We show that the XYZ spin chain along the special line of couplings J_xJ_y+J_xJ_z+J_yJ_z=0 possesses a hidden N=(2,2) supersymmetry. This lattice supersymmetry is non-local and changes the number of sites. It extends to the full transfer…

The general eight-vertex model on a square lattice is studied numerically by using the Corner Transfer Matrix Renormalization Group method. The method is tested on the symmetric (zero-field) version of the model, the obtained dependence of…

The Q matrix invented by Baxter in 1972 to solve the eight vertex model at roots of unity exists for all values of N, the number of sites in the chain, but only for a subset of roots of unity. We show in this paper that a new Q matrix,…

Following Baxter's method of producing Q_{72}-operator, we construct the Q-operator of the root-of-unity eight-vertex model for the crossing parameter $\eta = \frac{2m K}{N}$ with odd $N$ where Q_{72} does not exist. We use this new…

We study the two-dimensional Potts model on the square lattice in the presence of quenched random-bond impurities. For q>4 the first-order transitions of the pure model are softened due to the impurities, and we determine the resulting…

We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these…

We investigate the problem of mapping, through the Morita equivalence, odd dimensional noncommutative lattice gauge theories onto suitable matrix models. We specialize our analysis to noncommutative three dimensional QED (NCQED) and scalar…

We survey and enlarge the known mappings of the 16-vertex model, with emphasis on mappings between the even and odd 8-vertex subcases of the general model, also giving new mappings between these models, valid on finite toroidal lattices. In…

Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that when the deformation parameter q is equal to e^{+- 2 pi i/3}…

An $U_q(sl(n))$ invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of $q$ being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model…

In this paper we investigate the integrability properties of a two-state vertex model on the square lattice whose microstates at a vertex has always an odd number of incoming or outcoming arrows. This model was named odd eight-vertex model…

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…

In this work we propose a mechanism for converting the spectral problem of vertex models transfer matrices into the solution of certain linear partial differential equations. This mechanism is illustrated for the…

The exact solution is obtained for the eigenvalues and eigenvectors of the row-to-row transfer matrix of a two-dimensional vertex model with unlimited number of states per bond. This model is a classical counterpart of a quantum spin chain…

Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is given depending on a new free parameter. Specializing this…

We consider the symmetric two-state 16-vertex model on the square lattice whose vertex weights are invariant under any permutation of adjacent edge states. The vertex-weight parameters are restricted to a critical manifold which is…

At roots of unity the $N$-state integrable chiral Potts model and the six-vertex model descend from each other with the $\tau_2$ model as the intermediate. We shall discuss how different gauge choices in the six-vertex model lead to two…