R. L. Dobrushin

Wulff construction : a global shape from local interaction

Introduction Extremal properties of the Wulff functional Limit theorems Surface tension Large contours Proof of the main results.

A microscopic justification of the Wulff construction

We report results about a rigorous microscopic justification of the Wulff construction for the two-dimensional Ising model at low temperatures and under periodic boundary conditions. The idea of the proof is sketched.

Droplet Condensation in the Ising Model: Moderate Deviations Point of View

The threshold for the condensation of the vapour of microscopic droplets into a macroscopic one is studied for the case of the v-dimensional Ising model. The parameter which drives the condensation is the amount of the condensing phase, and the critical value of it, which turns the condensation on, is found to be of the order of IVNI(v-1)/v, where ∣VN∣ is the volume of the system. The corresponding behaviour of large and moderate deviations is studied. The principle of large deviations in the strong form is obtained in the region where condensation does not take place.