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:
Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <> 
Announcement from: Amir Yehudayoff   <>