Yinon Spinka (Tel Aviv)

Title: Long-range order in random 3-colorings

When: Martedi' 19 Maggio 2015 ORE 14:00

Where: Dipartimento di Matematica e Fisica Universita' degli Studi Roma Tre AULA 311 (SEMINARI), Largo San L. Murialdo, 1

Abstract: We study the anti-ferromagnetic 3-state Potts model of statistical physics. In this model, one samples a random coloring of a box in Z^d with 3 colors, with the probability of a coloring f being proportional to exp(-beta*N(f)), where beta>0 is a parameter (representing the inverse temperature) and N(f) is the number of edges connecting vertices colored with the same color. Our main result is that in high dimensions and low temperature (large beta), a sampled coloring will typically exhibit long-range order, placing the same color at most of either the even or odd vertices of the box. This extends previous work of Galvin, Kahn, Peled, Randall and Sorkin. The main ingredient in our proof is a new structure theorem for 3-colorings which characterizes the ways in which different "phases" may interact, putting special emphasis on the role of edges connecting vertices of the same color. We also discuss several related conjectures. No background in statistical physics will be assumed and all terms will be explained. Joint work with Ohad Feldheim.