When:	Mercoledì 2 Maggio 2007, ore 13.00
Where:	Aula 1101, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Who:	Prof. Thierry Gobron, CNRS - Université de Cergy Pontoise
Title:	Self-dual embeddings of graphs and Kramers-Wannier symmetry in non-planar Ising models
Abstract:	In this work, we consider the problem of constructing Ising models on non planar graphs (e.g. in D=3) which partition function exhibits a Kramers-Wannier symmetry between high and low temperature expansions, and which, according to classical arguments, possibly undergo a phase transition at temperature T_o=2/log(1+sqrt(2)). In a first part, we derive a "cut-and paste theorem" which allows for the construction of self-dual embeddings by pasting together embeddings of smaller graphs. As examples of application, we consider both the BCC and FCC lattices. In a second part, we show how to construct Ising models on graphs with a self dual embedding, in such a way that the low and high temperature expansions of their partition functions coincide through a Kramers-Wannier duality transformation. We discuss various features of these models and present preliminary numerical simulations indicating the existence of a first order phase transition at T_o for a model on the BCC lattice.