Statistical Physics of Non-Thermal Phase Transitions by Sergey G. Abaimov

Author:Sergey G. Abaimov
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.37)

The solution of this equation is

(4.38)

In the result, the size of a cluster to which site A belongs is zero if site A is empty with probability or and if site A is occupied with probability p:

(4.39)

In the limit , expanding (4.39), we find

(4.40)

which returns for the Bethe lattice.

Next, let us find the cluster-size distribution. For 1-clusters, we easily obtain

(4.41)

as the probability for the site to be occupied while all its neighbors are empty (Fig. 4.6a).

Fig. 4.6Normalized cluster number. a A 1-cluster. b A 2-cluster. c When we are increasing the size of a cluster, its perimeter loses site A that becomes occupied but gains the outer neighbors B and C of this site

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.