I will present new results on Glauber dynamics for the ferromagnetic Random Field Ising Model (RFIM) in Z^d. Of particular interest is a region of the phase diagram called the Griffiths phase where correlations decay exponentially fast on average over the random field, but there exists arbitrarily large islands of weak fields where low temperature behavior takes place, and quenched correlations do not decay. We prove a weak Poincaré inequality, implying that the dynamics relax in polynomial time in the volume of the domain and that efficient samplers exist in this regime. The proof combines ideas from stochastic analysis with coarse graining techniques.
This is based on joint work with Ronen Eldan, Reza Gheissari, and Arianna Piana.