Ornstein-Zernike theory of Ising and Potts models: a review of some applications (Yvan Velenik, Université de Genève)

09.10.2017 15:15

In this talk, I'll present a non-technical review of some of the results that have been obtained for Ising and Potts models on Z^d, using the so-called Ornstein-Zernike theory. The latter, among other applications, enables a non-perturbative analysis of these models, away from their critical point. The first class of results that will be discussed apply for all temperatures above the critical one, in any dimension: sharp asymptotics of spin-spin correlations and the effect of a line of modified coupling constants on the correlation length. The second class is restricted to two-dimensional models and applies to any temperature below critical: description of typical local behavior under arbitrary boundary condition; smoothness and strict convexity of the (Wulff) equilibrium crystal shape; Brownian bridge asymptotics for the interface; interface localization by a row of weakened coupling constants; scaling limit, as phase coexistence is approached, of the interface separating a layer of unstable phase along the boundary of the system from the stable phase occupying the bulk.
This talk will be based on a series of works done with various collaborators over the past 10-15 years.

Lieu

Room 17, Séminaire "Mathématique Physique"

entrée libre