Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 107, Issue 3-4, Pages 757-779Publisher
KLUWER ACADEMIC/PLENUM PUBL
DOI: 10.1023/A:1014586130046
Keywords
metastability; Markov chains; Glauber dynamics; kinetic Ising model
Categories
Ask authors/readers for more resources
We consider Glauber dynamics of classical spin systems of Ising type in the limit when the temperature tends to zero in finite volume. We show that information on the structure of the most profound minima and the connecting saddle points of the Hamiltonian can be translated into sharp estimates on the distribution of the times of metastable transitions between such minima as well as the low lying spectrum of the generator. In contrast with earlier results on such problems, where only the asymptotics of the exponential rates is obtained, we compute the precise pre-factors up to multiplicative errors that tend to I as T down arrow 0. As an example we treat the nearest neighbor Ising model on the 2 and 3 dimensional square lattice. Our results improve considerably earlier estimates obtained by Neves-Schonmann,((1)) Ben Arous-Cerf,((2)) and Alonso-Cerf.((3)) Our results employ the methods introduced by Bovier, Eckhoff, Gayrard, and Klein in refs. 4 and 5.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available