Title: Lee-Yang zeros and rational dynamics in two variables
Speaker: Roland Roeder
Speaker Info: IUPUI
In a classical work, Yang and Lee proved that zeros of certain polynomials (partition functions of Ising models) always lie on the unit circle. Distribution of these zeros control phase transitions in the model. We study this distribution for a special "Migdal-Kadanoff hierarchical lattice". In this case, it can be described in terms of the dynamics of an explicit rational function in two variables.Date: Tuesday, October 27, 2009
More specifically, we prove that the renormalization operator is partially hyperbolic and has a unique central foliation. The limiting distribution of Lee-Yang zeros is described by a holonomy invariant measure on this foliation. I will explain both of the above (omiting some details) and then show how questions about the critical exponents and local structure of the zeros are related to the dynamics of the renormalization map.
This is a joint work with Pavel Bleher and Mikhail Lyubich.