Student Probability/PDE Seminar: A Condition for Long-Range Order in Discrete Spin Systems

Seminar | September 29 | 2:10-3:30 p.m. | 891 Evans Hall

 Yinon Spinka, Tel-Aviv University

 Department of Mathematics

We present a new condition for the existence of long-range order in discrete spin systems, which emphasizes the role of entropy and high dimension. The condition applies to all symmetric nearest-neighbor discrete spin systems with an internal symmetry of `dominant phases'. Specific applications include a proof of Kotecky's conjecture (1985) on anti-ferromagnetic Potts models, a strengthening of results of Lebowitz-Gallavotti (1971) and Runnels-Lebowitz (1975) on Widom-Rowlinson models and of Burton-Steif (1994) on shifts of finite type, and a significant extension of results of Engbers-Galvin (2012) on random graph homomorphisms on the hypercube. No background in statistical physics will be assumed and all terms will be explained thoroughly. Joint work with Ron Peled.