The loop O(n) model and the XOR trick
Matan Harel (Northeastern University)
Abstract: The loop O(n) model is a model for random configurations of non-overlapping loops on the hexagonal lattice, which contains many models of interest (such as the Ising model, self-avoiding walks, and random Lipshitz functions) as special cases. The physics literature conjectures that the model undergoes several different phase transitions, leading to a dazzling phase diagram; over the last several years, several features of the phase diagram have been proven rigorously. In this talk, I will describe the predicted behavior of the model and show some recent progress towards proving that typical samples of perturbations of the uniform measure on loop configurations have long loops. This is joint work with Nick Crawford, Alexander Glazman, and Ron Peled.
mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry
Audience: researchers in the topic
Geometry, Physics, and Representation Theory Seminar
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