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Physica A Statistical Mechanics and its Applications

Critical behavior in anisotropic cubic systems with long-range interactions

Yoshitake Yamazaki

Published Mar 1, 1978• 6 citations
Publisher
DOI
10.1016/0378-4371(78)90007-9

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Critical behavior in anisotropic cubic systems with the short-range interaction is studied by means of the Callan-Symanzik equations. As the static critical behavior, the stability of fixed points, the critical exponents ηC, γC, φsC and φcC, etc. are investigated. As the dynamic critical behavior, the dynamic critical exponent zφ is derived on the basis of the time dependent Ginzburg-Landau stochastic model. New results are a correction term of order ε3 in ηC, the crossover index φsC and the dynamic critical exponent zφ.

Progress of Theoretical Physics•Jun 1, 1976•16 citations
The renormalization group approach is applied to the study of the short-time critical behaviour of the d -dimensional n -component anisotropic cubic spin systems with long-range interaction of the form p σ s p s - p in momentum space. Firstly, the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents θ' and θ of the order parameter and the response function, respectively, are calculated to the second order in = 2σ- d . For 1⩽ d <2σ and n > n c , the cubic anisotropy affects the short-time critical behaviour.
Critical behavior in anisotropic cubic systems with the short-range interaction is studied by means of the Callan-Symanzik equations. As the static critical behavior, the stability of fixed points, the critical exponents ηC, γC, φsC and φcC, etc. are investigated. As the dynamic critical behavior, the dynamic critical exponent zφ is derived on the basis of the time dependent Ginzburg-Landau stochastic model. New results are a correction term of order ε3 in ηC, the crossover index φsC and the dynamic critical exponent zφ.