| 概要 | In this talk we detail recent and ongoing work on randomness induced ordering is statistical mechanics.
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 may be viewed as a classical, many body analog of the well known phenomenon of Anderson Localization.
In this talk we will explain why this is a remarkable question even at the classical level and detail partial answers recently obtained. |