This volume is a synopsis of recent works aiming at a mathematically rigorous justification of the phase coexistence phenomenon, starting from a microscopic model. It is intended to be self-contained. Those proofs that can be found only in research papers have been included, whereas results for which the proofs can be found in classical textbooks are only quoted.

Inhalt

Phase coexistence and subadditivity.- Presentation of the models.- Ising model.- Bernoulli percolation.- FK or random cluster model.- Main results.- The Wulff crystal.- Large deviation principles.- Large deviation theory.- Surface large deviation principles.- Volume large deviations.- Fundamental probabilistic estimates.- Coarse graining.- Decoupling.- Surface tension.- Interface estimate.- Basic geometric tools.- Sets of finite perimeter.- Surface energy.- The Wulff theorem.- Final steps of the proofs.- LDP for the cluster shapes.- Enhanced upper bound.- LDP for FK percolation.- LDP for Ising.