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Spring Topology and Dynamical Systems Conference 2008
March 13-15, 2008
University of Wisconsin Milwaukee and Marquette University
Milwaukee, WI, USA

Organizers
Ric Ancel, Karen Brucks, Craig Guilbault, Chris Hruska, Suzanne Hruska, Boris Okun (UWM); Paul Bankston (Marquette); Lois Kailhofer (Alverno College).

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Complex dynamics for the Lee-Yang zeros
by
Roland Roeder
U. Toronto
Coauthors: Pavel Bleher and Mikhail Lyubich

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. We show that the Yang-Lee zeros are organized in a transverse measure for a dynamical foliation on an invariant cylinder. From the complex point of view, they get interpreted as slices of a dynamical (1,1)-current on the projective space.

Date received: February 11, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawk-40.