Large deviations in the van der Waals limit
The main result is a strong large deviation principle for the empirical distribution of Ising spins in the 2-dimensional Ising system with the Kac potential and the scaling parameter \(\gamma \) at temperatures less than the critical one. It is studied in the thermodynamic limit followed by the limit for the scaling parameter \(\gamma >0\) tending to zero. Results of the paper by the authors and \textit{P. Buttà} [Markov Process. Relat. Fields 3, No. 2, 175-198 (1997; Zbl 0910.60014)], where interfaces were studied and a weak form of the large deviation principle was established, are used. The proof of the strong version needs moreover an estimate called ``exponential tightness''. Its proof is based on a reformulation in terms of contours for some auxiliary block-spin model, the study of contours, and some Peierls estimates.
scientific article; zbMATH DE number 1364474
scientific article