Presented by: 
Roland Roeder (Indiana University-Purdue University Indianapolis)
Mon 17 Jun, 2:00 pm - 3:00 pm
Priestley 67-442

In a classical work, Lee and Yang 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. 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. These results follow from a general
principal of expressing the Lee-Yang zeros for a hierarchical lattice
in terms of expanding Blaschke products allowing for generalization to
many other hierarchical lattices. This is joint work with Pavel
Bleher and Misha Lyubich.