期刊
JOURNAL OF STATISTICAL PHYSICS
卷 125, 期 1, 页码 22-54出版社
SPRINGER
DOI: 10.1007/s10955-006-9175-y
关键词
glass transition; Glauber dynamics; correlation time; correlation length
Glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order. It is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length. We prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases. Our results are valid in a rather general setting, which covers finite-dimensional and mean field systems. As an illustration, we discuss the Glauber (heat bath) dynamics of p-spin glass models on random regular graphs. We present the first proof that a model of this type undergoes a purely dynamical phase transition not accompanied by any thermodynamic singularity.
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