Oct 20, 3:30pm, Wean 8220

Ohad Feldheim, Tel Aviv University

Rigidity of 3-colorings of the d-dimensional discrete torus

Ohad Feldheim, Tel Aviv University

Rigidity of 3-colorings of the d-dimensional discrete torus

Abstract:

We prove that a uniformly chosen proper coloring of Z_{2n}^d with
3 colors has a very rigid structure when the dimension d is sufficiently
high. The coloring takes one color on almost all of either the even or the
odd sub-lattice. In particular, one color appears on nearly half of the
lattice sites. This model is the zero temperature case of the 3-states
anti-ferromagnetic Potts model, which has been studied extensively in
statistical mechanics. The proof involves results about graph homomorphisms
and various combinatorial methods, and follows a topological intuition.
Joint work with Ron Peled.