Large-scale behavior of the Villain model at low temperature in d = 3

Abstract: In this talk, we will study the Villain rotator model in dimension three and prove that, at low temperature, the truncated two-point function of the model decays asymptotically like $|x|^{2-d}$, with an algebraic rate of convergence. The argument starts from the observation that the asymptotic properties of the Villain model are related to the large-scale behavior of a vector-valued random surface with uniformly elliptic and infinite range potential, following the arguments of Fröhlich, Spencer and Bauerschmidt. We will then see that this behavior can be studied quantitatively by combining two sets of tools: the Helffer-Sjöstrand PDE, initially introduced by Naddaf and Spencer to identify the scaling limit of the discrete Ginzburg-Landau model, and the techniques of the quantitative theory of stochastic homogenization developed by Armstrong, Kuusi and Mourrat. Joint work with Wei Wu.

dynamical systemsprobability

Audience: researchers in the topic

( paper | slides | video )

Horowitz seminar on probability, ergodic theory and dynamical systems