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Phys Rev E Stat Nonlin Soft Matter Phys. 2005 Feb;71(2 Pt 2):026130. Epub 2005 Feb 28.

Dynamical real-space renormalization group calculations with a highly connected clustering scheme on disordered networks.

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  • 1Department of Physics, Faculty of Sciences and Letters, Istanbul Technical University, Maslak 34469, Istanbul, Turkey.


We have defined a type of clustering scheme preserving the connectivity of the nodes in a network, ignored by the conventional Migdal-Kadanoff bond moving process. In high dimensions, our clustering scheme performs better for correlation length and dynamical critical exponents than the conventional Migdal-Kadanoff bond moving scheme. In two and three dimensions we find the dynamical critical exponents for the kinetic Ising model to be z=2.13 and z=2.09 , respectively, at the pure Ising fixed point. These values are in very good agreement with recent Monte Carlo results. We investigate the phase diagram and the critical behavior of randomly bond diluted lattices in d=2 and 3 in the light of this transformation. We also provide exact correlation exponent and dynamical critical exponent values on hierarchical lattices with power-law and Poissonian degree distributions.

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