Cluster Variational Method in Edwards-Anderson 2D: single instance and average case

by Alejandro Lage Castellanos (Havana University, Cuba)

Wednesday 15 Feb 2012, 15:00 → 17:00 Europe/Rome

Aula Careri (Dip. di Fisica - Edificio G. Marconi)

We study the plaquette-CVM approximation to the free energy of the EA 2D model. It improves Bethe approximation in more than one way. The prediction of the transition temperature is lower (should be zero) and the correlations infered in the paramagnetic phase is in good correspondence with Monte Carlo simulations. At variance with the standard Bethe approximation in random graphs, there are two different ways of approaching an average case study of the system. A population dynamics iterative algorithm a la Bethe-Peirels correctly locates the appearance of spin glass solutions in the single instance, while a replica-CVM instability calculation correctly predicts the loss of convergence of the algorithm. While in Bethe approximation both procedures are equivalent and both things occur at the same temperature, in plaquette-CVM approximation they are different,and the algorithm can study a small window of non paramagnetic solutions, that we guess are related to dynamic properties of the system.