We describe birational representations of discrete groups generated by involutions, having their origin in the theory of exactly solvable vertex-models in lattice statistical mechanics. These involutions correspond respectively to two kinds of transformations on q × q matrices: the inversion of...

We propose a conjecture for the exact expression of the unweighted dynamical zeta function for a family of birational transformations of two variables, depending on two parameters. This conjectured function is a simple rational expression with integer coefficients. This yields an algebraic value...

We analyse the properties of a particular birational mapping of two variables (Cremona transformation) depending on two free parameters (ε and α), associated with the action of a discrete group of non-linear (birational) transformations on the entries of a q × q matrix. This mapping...

We consider a family of birational transformations of two variables, depending on one parameter, for which simple rational expressions with integer coefficients, for the exact expression of the dynamical zeta function, have been conjectured. Moreover, an equality between the (asymptotic of the)...

We study the phase diagram of an isotropic six-state chiral Potts model on a square lattice by means of both exact and numerical methods. The phase diagram of this model presents many similarities with the phase diagrams of the Ashkin-Teller model or the models studied by Zamolodchikov and...

We consider the q-state Potts model on the triangular lattice with two- and three-site interactions in alternate triangular faces, and determine zeroes of the partition function numerically in the case of pure three-site interactions. On the basis of a rigorous reciprocal symmetry and results on...

We sketch a subset of Professor F.Y. Wu's contributions in lattice statistical mechanics, solid state physics, graph theory, enumerative combinatorics and other domains of physics and mathematics. We will recall some of F.Y. Wu's most important and well-known classic results and we will also...

We study birational mappings generated by matrix inversion and permutation of the entries of q × q matrices. For q = 3 we have performed a systematic examination of all the permutations of 3 × 3 matrices in order to find integrable mappings (of three different kinds) and finite order mappings....