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.