CELL-TO-SITE RENORMALIZATION GROUP STUDY OF A SANDPILE

An-Chung Cheng, Chien-Fu Chen and Chai-Yu Lin ()
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An-Chung Cheng: Department of Physics, National Chung Cheng University, Chia-Yi 66117, Taiwan, R. O. C.
Chien-Fu Chen: Department of Physics, National Chung Cheng University, Chia-Yi 66117, Taiwan, R. O. C.
Chai-Yu Lin: Department of Physics, National Chung Cheng University, Chia-Yi 66117, Taiwan, R. O. C.

International Journal of Modern Physics C (IJMPC), 2008, vol. 19, issue 11, 1695-1703

Abstract: This study investigates the Bak–Tang–Wiesenfeld sandpile using a renormalization group (RG) approach based on the similarity ofL × LRG cells of different scales. The fundamental difficulty of this approach arises from the lack of full enumeration of all relaxations inside a RG cell asL ≥ 3. This study develops a simple sampling algorithm to sample the relaxations and applies this algorithm to the RG calculations forL = 3, 4, and 8. As the fixed point analysis shows, increasingLdoes not lead the resultant height probabilities toward the exact solution.

Keywords: Self-organized criticality; BTW sandpile; renormalization group; simple sampling; 05.50.+q; 05.65.+b (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1142/S0129183108013229

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