The Real Space Dynamic Renormalization Group

Mazenko, Gene F.; Valls, Oriol T.

doi:10.1007/978-3-642-81825-7_4

Cited by 1 publication

(2 citation statements)

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“…The relevant difference between our scheme and other dynamical RG methods is the fact that we obtain a set of equations which are independent on the specific form of the stationary probability distribution of the system. This perspective is quite different from several previous real space dynamical RG approaches which were based on the explicit knowledge of the stationary distribution or the detailed balance hypothesis [31]. The application range of these methods was therefore restricted to to the relaxation dynamics of equilibrium systems.…”

Section: Driving Condition and Recursion Relationsmentioning

confidence: 92%

“…The time scaling is chosen so that it keeps the equations in the same form. A different formalism, suitable to study the properties of the model even far from the critical region, was developed by Mazenko et al [31] The coarse graining operator and the time rescaling are chosen self-consistently in order to insure the Markoffian behavior of the renormalized spin flip operator. One then writes recursion relations for the two-point correlation functions from which the critical properties of the model are extracted.…”

Section: Coarse Graining and Renormalizationmentioning

confidence: 99%

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Dynamically driven renormalization group

1997

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We present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed

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Section: Driving Condition and Recursion Relationsmentioning

confidence: 92%

Section: Coarse Graining and Renormalizationmentioning

confidence: 99%