Metastability in the dilute Ising model

Stochastic Analysis Seminar Series

Consider Glauber dynamic for the Ising model on the hypercubic lattice with a positive magnetic field. Starting from the minus configuration, the system initially settles into a metastable state with negative magnetization. Slowly the system relaxes to a stable state with positive magnetization. Schonmann and Shlosman showed that in the two dimensional case the relaxation time is a simple function of the energy required to create a critical Wulff droplet. The dilute Ising model is obtained from the regular Ising model by deleting a fraction of the edges of the underlying graph. This produces a catalyst effect.

Even an arbitrarily small dilution can dramatically reduce the relaxation time. Joint work with Thierry Bodineau and Marc Wouts.


Ben Graham (University of Warwick)

Monday, January 23, 2012 - 14:15
to 15:15