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Short‐Time Critical Behavior of Systems with Random Impurities
Author(s) -
Chen Y.,
Guo S.H.,
Li Z.B.
Publication year - 2001
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(200102)223:3<599::aid-pssb599>3.0.co;2-l
Subject(s) - statistical physics , autocorrelation , scaling , exponent , logarithm , mathematics , renormalization group , critical exponent , critical dimension , exponential function , physics , condensed matter physics , mathematical physics , mathematical analysis , statistics , linguistics , geometry , philosophy
The theoretical renormalization‐group approach is applied to the study of the short‐time critical behavior of the Ginzburg‐Landau model with long‐range random impurities which have a power‐like correlation r —( d — ρ . The system initially at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with a model A dynamics. The asymptotic scaling laws are studied in the frame of a double expansion in ϵ = 4 — d and δ = ϵ + ρ with δ of the order of ϵ . The initial slip exponent θ ′ for the order parameter is calculated up to the first order in ϵ = 4 — d or in ϵ 1/2 corresponding to different fixed points, respectively. For d > 4, the short‐time behavior of the order parameter is investigated in one loop. Two different logarithmic and exponential‐logarithmic corrections to short‐time behaviors of both the autocorrelation and the order parameter are also solved in d = 4 dimension. Crossover between the nonrandom behavior and quenched behavior is found for n = 4 (where n is the spin dimensionality) in d = 4 dimension.