Universality, Renormalization Group and Kadanoff relations

by Prof. Vieri Mastropietro (Università di Milano)

Thursday 11 Mar 2021, 15:00 → 16:00 Europe/Rome

Abstract:

Universality, stating the independence from microscopic details of certain macroscopic quantities, is a crucial concept, with deep implications ranging from statistical physics to Quantum Field Theory. I will start considering basic statistical mechanics models, like interacting Ising, vertex and dimer models. Universality in this class of systems has the form of  Kadanoff relations between the exponents governing the critical behaviour; some of such relations have been checked in special solvable cases but a mathematical proof that they hold generically has been elusive for several years. Only recently the methods of rigorous Renormalization Group have allowed a proof of several such universal relations even in absence of exact solutions, and i will review the main results, the methods for achieving them and the open problems. Finally the strict relation between universality in statistical physics and certain deep features in Quantum Field Theory will be recalled.