Renormalization-group approach to the Manna sandpile.
In this paper a renormalization group (RG) scheme for the q -state Manna model is proposed based on the stochastic characteristic and the similarity of topplings at different scales. A full enumeration of the RG evolution events inside a 2 x 2 RG cell for q=2 , 3, and 4 was carried out. A fixed point analysis shows that the resulting height probabilities are very close to the results obtained by the numerical simulations. The calculations of the toppling number exponent tau and the dynamical exponent z are also provided. It was found that the RG values of tau and z for q=4 are very close to the simulation values.
Lin
Chai-Yu
CY
Department of Physics, National Chung Cheng University, Chia-Yi 62102, Taiwan and National Center for Theoretical Sciences at Taipei, Physics Division, National Taiwan University, Taipei 10617, Taiwan.