Loop Models in 2d Statistical Mechanics
Many 2d planar lattice models may be realized as random non-intersecting nested loops. In the $O(n)$ model, each loop has a weight given by a real positive number $n$. These weights are non-local and one may ask whether there is a local updating algorithm to simulate such an ensemble. The answer is yes, if $n=2\cos(\pi/m)$ with $m$ an integer $\geq3$. At the critical point the scaling limit of this loop gas is called the Conformal Loop Ensemble, and I shall discuss some if its known and conjectured properties.
Refreshments in Math Commons Room at 3:30pm