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Herald of Omsk University Series Psychology

Ренормгрупповое описание неравновесной критической релаксации однородных систем в трехпетлевом приближении

Ivan A. Kalashnikov, Vladimir V. Prudnikov, Pavel Vladimirovich Prudnikov, Stepan S. Tsirkin

Published Jan 1, 2007• 0 citations
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Abstract

The theoretical-field renormalization group description of nonequilibrium initial states influence on critical evolution of order parameter is offered. The dissipative relaxation behavior (model A) is considered to obtain the initial slip exponent θ for pure systems with n-component order parameter. Exponent θ is calculated in three-loop approximation

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The theoretical-field renormalization group description of nonequilibrium initial states influence on critical evolution of order parameter is offered. The dissipative relaxation behavior (model A) is considered to obtain the initial slip exponent θ for pure systems with n-component order parameter. Exponent θ is calculated in three-loop approximation
The influence of nonequilibrium initial values of the order parameter on its evolution at a critical point is described using a renormalization group approach of the field theory. The dynamic critical exponent θ of the short time evolution of a system with an n -component order parameter is calculated within a dynamical dissipative model using the method of Σ-expansion in a three-loop approximation. Numerical values of θ for three-dimensional systems are determined using the Padé-Borel method for the summation of asymptotic series.
The relaxational models introduced in a previous treatment of critical dynamics are studied in detail using renormalization-group methods. The earlier results are justified by an analysis to all order in $\ensuremath{\epsilon}=4\ensuremath{-}d$, where ddd is the dimensionality. The diagrammatic formalism of the full dynamic renormalization group is presented, and applied to the earlier models. A generalization of Wilson's Feynman-graph expansion method is used to calculate the exponents to second order in $\ensuremath{\epsilon}$. In model CCC, where a nonconserved order parameter is coupled to a conserved energy field, ambiguities were found in the earlier recursion-relation treatment for 2<n<42<n<42<n<4, $d\ensuremath{\approx}4$ (nnn is the number of components of the order parameter). These ambiguities are discussed in the present work, but are not fully resolved.
Ренормгрупповое описание неравновесной критической динамики спиновых систем при фиксированной размерности пространства d=3d=3d=3
Представлены методика и результаты ренормгруппового описания неравновесной критической релаксации модели А с эволюцией из начального высокотемпературного состояния. Рассчитана двухвременная зависимость для корреляционной функции и функции отклика и выявлены нарушения флуктуационно-диссипативной теоремы в неравновесном критическом режиме. Для предельного флуктуационно-диссипативного отношения, являющегося универсальной характеристикой неравновесной критической динамики, проведен в двухпетлевом приближении расчет флуктуационных и примесных поправок при фиксированной размерности пространства d=3d=3d=3 с применением методов суммирования асимптотических рядов Паде-Бореля.