Dynamics and Renormalization Seminar
Wednesday January 27th, 2021
Time: 2:30 PM - 3:30 PM
Title: Mini-course. Renormalization Group and Critical Phenomena in Hierarchical Models of Statistical Physics
Speaker: Roland Roeder, IUPUI
Abstract:
In the series of four lectures we will discuss various results on renormalization group (RG) and critical phenomena in hierarchical models. We will consider two different types of hierarchical models:
1. Dyson's hierarchical models,
2. Migdal-Kadanoff's spin models on hierarchical lattices.
The great importance of hierarchical models is that they allow investigation of various phenomena unavailable in other models. We will discuss evaluation of critical exponents, phase transitions in models with discrete and continuous symmetry, Fisher's and Lee-Yang's zeros, and others. For Dyson's hierarchical models the RG action is described in terms of a nonlinear integral operators, and we will explain a technique to investigate this nonlinear dynamics. For Migdal-Kadanoff's spin models on hierarchical lattices the RG action is described in terms of rational mappings in one and two dimensions, and we will find their attractors and the limiting Lee-Yang measures in dimension 1 and the limiting Fisher-Lee-Yang currents in dimension 2.
Part I of the lectures will be based on the works of Bleher-Sinai and Bleher-Major, and Part II on the works of Bleher-Lyubich-Roeder.