Speaker :	Mr. Wei-Kuo Chen (University of California, Irvine)
Title :	On the Mixed Even-Spin Sherrington-Kirkpatrick Model with Ferromagnetic Interaction
Time :	2011-07-08 (Fri) 10:00 - 12:00
Place :	Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract:	We study the mixed even-spin Sherrington-Kirkpatrick (SK) model with ferro¬magnetic interaction and parallel many well-known behaviors of the SK model to our model. Our main results are: (i) The thermodynamic limit of the free energy exists and can be represented in terms of the thermodynamic limit of the free en¬ergy of the SK model with a variation of external fields. In the presence of the centered Gaussian external field, (ii) on a dense subset of the inverse tempera¬ture parameter the overlap is positive and the Gibbs measures satisfy the extended Ghirlanda-Guerra identities, and (iii) we depict a region for the inverse temperature parameter on which the overlap can be controlled quantitatively away from the ori¬gin by the magnetization. Our approach is based on the techniques from the study of the Curie-Weiss model and also remarkable results in convex analysis.