2010/01/19 by Su‐Chan Park, Park, Su-Chan
Earth and Planetary Sciences · Materials Science · Physics and Astronomy · #FOS: Physical sciences #Geological formations and processes #Material Dynamics and Properties #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.1001.3359
openalex publication_date 2010/01/19 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
We investigate the origin of the difference, which was noticed by Fey it et\nal. [Phys. Rev. Lett. bf 104, 145703 (2010)], between the steady state\ndensity of an Abelian sandpile model (ASM) and the transition point of its\ncorresponding deterministic fixed-energy sandpile model (DFES). Being\ndeterministic, the configuration space of a DFES can be divided into two\ndisjoint classes such that every configuration in one class should evolve into\none of absorbing states, whereas no configurations in the other class can reach\nan absorbing state. Since the two classes are separated in terms of toppling\ndynamics, the system can be made to exhibit an absorbing phase transition (APT)\nat various points that depend on the initial probability distribution of the\nconfigurations. Furthermore, we show that in general the transition point also\ndepends on whether an infinite-size limit is taken before or after the\ninfinite-time limit. To demonstrate, we numerically study the two-dimensional\nDFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there\nare indeed many thresholds. Nonetheless, the critical phenomena at various\ntransition points are found to be universal. We furthermore discuss a\nmicroscopic absorbing phase transition, or a so-called spreading dynamics, of\nthe BTW-FES, to find that the phase transition in this setting is related to\nthe dynamical isotropic percolation process rather than self-organized\ncriticality. In particular, we argue that choosing recurrent configurations of\nthe corresponding ASM as an initial configuration does not allow for a\nnontrivial APT in the DFES.\n