Technion Mathematics Departement Colloquium Speaker: Nicholas Crawford (Technion) Title: Random Field Induced Ordering Time: Monday, October 31, 3:30 pm Place: Amado 232 Abstract: In this talk I will introduce a subject of current interest in mathematical and statistical physics. The paradigmatic, but by no means only, example is given the O(2) model in d dimensions with an additional local field term in the Hamiltonian given by i.i.d. unit vectors pointing in the North/South direction with equal probability. The question we are interested in is whether, for any sufficiently small local field strength, there is a temperature low enough so that sufficiently large block averages of spin variables typically have preferred orientations under the corresponding Gibbs measure. If so, what direction(s) are preferred? This question has connections to Anderson localization and Homogenization of PDEs among other topics. I will explain why this is a remarkable question and detail recent results resolving certain controversies on the subject. I will begin from the beginning, so no prior knowledge of anything mentioned above is assumed. ------------------------------------------------------------------- Visit our colloquim website: <http://www.technion.ac.il/~yehuday/colloquium/colloq.html> --------------------------------------------------------- Technion Math. Net (TECHMATH) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Amir Yehudayoff <amir.yehudayoff@gmail.com>