Sandpile Dynamics and Renormalization-group Approach
نویسنده
چکیده
A successful renormalization-group (RG) approach may provide signinicant insights of a system exhibiting power-law dependencies. In 1994, a RG scheme [1] was proposed for sandpile models which exhibit power-law behavior and function as the models of self-organized criticality [2]. One momentous result of such a RG approach is that BakTang-Wisenfeld (BTW) [2] sandpile posepossing a deterministic toppling rule and Manna sandpile [3] poseposing a stochastic toppling rule share the same universality calss. Such a conjecture is oppositive to the numerical results. To clear up the discrepancy, Lin et al. [4] developed a sampling procedure to sample the RG events. Based on such a sampling procedure, we propose a Monte Carlo RG approach to q-state Manna model and such a study will be a prescription to perform our RG results for the high q case. In this paper, we calculate the related physical quantities for q = 2, 3, 4, 6, 8, 12, 14, 16, and 20. The results of our RG approach can be used to inverestigate the universality issue of q-state Manna model and the key factor effecting the exponents.
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