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Reail Space Renormalization Group for Self Organized Criticality in Sandpile Models

Published online by Cambridge University Press:  03 September 2012

S. Zapperi ,
A. Vespignanit  and
L. Pietronero
S. Zapperi
Affiliation:
Center for Polymer Studies and Department of Physics, Boston University, Boston, MA 02215, USA
A. Vespignanit
Affiliation:
Department of Mathemathics, Yale University, New Haven, CT-06520-8283, USA
L. Pietronero
Affiliation:
Dipartimento di Fisica, Université di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, Italy
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Abstract

We have introduced a new renormalization group approach that allows us to describe the critical stationary state of sandpile models (Phys. Rev. Lett. 72, 1690 (1994)). We define a characterization of the phase space in order to study the evolution of the dynamics under a change of scale. We obtain a non trivial actractive fixed point for the parameters of the model that clarifys the self organized critical nature of these models. We are able to compute the values of the critical exponents and the results are in good agreement with computer simulations. The method can be naturally extended to several other problems with non equilibrium stationary state.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 367: Symposium P – Fractal Aspects of Materials , 1994 , 67
Copyright
Copyright © Materials Research Society 1995

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