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Cluster equations for the Glauber kinetic Ising ferromagnet: I. Existence and uniqueness
Author(s) -
Kreer Markus
Publication year - 1993
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19935050806
Subject(s) - glauber , uniqueness , ising model , cluster (spacecraft) , nucleation , detailed balance , ferromagnetism , kinetic energy , mathematical physics , physics , statistical physics , mathematics , mathematical analysis , quantum mechanics , thermodynamics , computer science , scattering , programming language
The infinite set of cluster equations, proposed by Binder and Müller‐Krumbhaar for a Glauber kinetic Ising ferromagnet in 1974, generalize the Becker‐Döring equations used in classical nucleation theory. For positive symmetric transition rates satisfying certain growth conditions and a detailed balance condition we prove for sufficiently fast decaying initial cluster distributions the existence of a positive cluster distribution with finite density for all finite times solving the cluster equations. Uniqueness is proven under some further conditions on the transition rates. Our existence and uniqueness results apply e.g. for a Glauber kinetic Ising ferromagnet in two dimensions.