Seminar: The Random Cluster Model: Phase transitions, Combinatorics, Algorithms
Department of Industrial Engineering
The Random Cluster Model: Phase transitions, Combinatorics, Algorithms
The Random Cluster model introduced by Fortuin and Kasteleyn, is a well known statistical physics model that contains the Ising and Potts models as special cases. Given a graph G, a probability p and a positive real parameter q, the random cluster model is a probability distribution on edge subgraphs on G that for q = 1 is bond percolation and for positive integers q > 1, is essentially the Potts model with q colours. Physicists are chiefly interested in the model for q > 1; When 0 < q < 1, the model has less physical significance, though it includes the case of the uniform spanning tree measure as a weak limit. The regime 0 < q < 1 has seen limited work, despite Kasteleyn having been personally interested in this problem.
In this talk, I will present a few results in this exotic q < 1 regime : These include correlation inequalities, an understanding of extremal configurations and some partial results on the existence of Gibbs measures. This is joint work with Recep Altar Ciceksiz.
Mohan Ravichandran got his PhD at the University of New Hampshire with a thesis in functional analysis. For the last five years, he has been working in discrete probability and combinatorics. He is currently interested in phase transitions in statistical physics and combinatorial techniques for understanding these. He has worked at the Mimar Sinan Fine Arts University and Bogazici University and has also held semester long visiting positions at the Simons Institute for the Theory of Computation at Berkeley and the Mittag-Leffler Institute in Stockholm.
Date: Friday, September 23, 2022.
Place: Engineering Building, South Campus, VYKM 2