Surface depinning under the two-dimensional hammock potential

Ron Peled , Tel Aviv University
Jadwin Hall A06

We consider a random two-dimensional surface satisfying a Lipschitz constraint. The surface is uniformly chosen from the set of all real-valued Lipschitz functions on a two-dimensional discrete torus. Our main result is that the surface delocalizes, having fluctuations whose variance is at least logarithmic in the size of the torus. Our technique follows closely the approach of Richthammer, who developed a variant of the Mermin-Wagner method applicable to hard-core constraints. The result answers an open question mentioned by Brascamp, Lieb and Lebowitz on the hammock potential. Extensions and related open problems will also be discussed. Joint work with Piotr Miłoś.