Potts models on Erdos-Renyi random graphs

Stochastics Seminar
Thursday, September 15, 2011 - 15:05
1 hour (actually 50 minutes)
Skiles 006
University of Rochester
The Potts antiferromagnet on a random graph is a model problem from disordered systems, statistical mechanics with random Hamiltonians. Bayati, Gamarnik and Tetali showed that the free energy exists in the thermodynamic limit, and demonstrated the applicability of an interpolation method similar to one used by Guerra and Toninelli, and Franz and Leone for spin glasses. With Contucci, Dommers and Giardina, we applied interpolation to find one-sided bounds for the free energy using the physicists' ``replica symmetric ansatz.'' We also showed that for sufficiently high temperatures, this ansatz is correct. I will describe these results and some open questions which may also be susceptible to the interpolation method.