CELL-TO-SITE RENORMALIZATION GROUP STUDY OF A SANDPILE

Abstract

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