Forbidden gap argument for phase transitions proved by means of chessboard estimates

Abstract

A weak version of completeness of phase diagram is proven with the help of chessboard estimates. For models depending on a parameter (say, the temperature), this means that the values of the conjugate thermodynamic quantity (the energy) inside the ''transitional gap'' are forbidden in all shift-ergodic Gibbs states.

Keywords

• phase transitions
• lattice models
• reflection positivity
• chessboard estimates