Lectures on Glauber dynamics for discrete spin models

These notes have been the subject of a course I gave in the summer 1997 for the school in probability theory in Saint-Flour. I review in a self-contained way the state of the art, sometimes providing new and simpler proofs of the most relevant results, of the theory of Glauber dynamics for classical lattice spin models of statistical mechanics. The material covers the dynamics in the one phase region, in the presence of boundary phase transitions, in the phase coexistence region for the two dimensional Ising model and in the so-called Griffiths phase for random Systems.

[1]  Palmer,et al.  Low-frequency relaxation in Ising spin-glasses. , 1985, Physical review letters.

[2]  J. Chayes,et al.  The phase boundary in dilute and random Ising and Potts ferromagnets , 1987 .

[3]  A. Bray.  Upper and lower bounds on dynamic correlations in the Griffiths phase , 1989 .

[4]  Pierre Picco,et al.  Cluster expansion ford-dimensional lattice systems and finite-volume factorization properties , 1990 .

[5]  D. Stroock,et al.  The logarithmic sobolev inequality for discrete spin systems on a lattice , 1992 .

[6]  F. Martinelli,et al.  Approach to equilibrium of Glauber dynamics in the one phase region , 1994 .

[7]  Strong decay to equilibrium in one-dimensional random spin systems , 1994 .

[8]  R. H. Schonmann,et al.  Lifshitz' law for the volume of a two-dimensional droplet at zero temperature , 1995 .

[9]  Local Analyticity and bounds on the truncated correlation functions in disordered systems , 1995 .

[10]  F. Martinelli,et al.  On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results , 1996 .

[11]  C. Maes,et al.  Percolation techniques in disordered spin flip dynamics: Relation to the unique invariant measure , 1996 .

[12]  Decay to equilibrium in random spin systems on a lattice. II , 1996 .

[13]  On the layering transition of an SOS surface interacting with a wall. II. The Glauber dynamics , 1996 .

[14]  Gustavo Posta.  Spectral gap for an unrestricted Kawasaki type dynamics , 1997 .

[15]  B. Zegarliński,et al.  Coercive Inequalities for Gibbs Measures , 1999 .