Alexander Glazman: 2D Potts model at a transition point

The q-state Potts model is a distribution on all possible colouring's of vertices of a box [-N,N]x[-N,N] in q colours that depends on a temperature T. It is classical that the model undergoes a phase transition at some T_c: when T<T_c, there is a giant monochromatic component (ordered regime); when T>T_c, there is exponential decay of correlations (disorder).

In this talk, we discuss the behaviour at T_c which is known to depend on q. When q ≤ 4, one should see random fractals in the limit (proven only at q=2 by Smirnov et al) and we explain a connection to random surface models via a Fourier transform. When q>4, we show convergence of interfaces between ordered and disordered parts to Brownian bridges. In particular, we establish the wetting phenomenon conjectured by Bricmont and Lebowitz in 1987.

Based on joint works with M. Dober and S. Ott, and with P. Lammers.