Absorbing phase transitions in deterministic fixed-energy sandpile models

Physical Review. E
Su-Chan Park

Abstract

We investigate the origin of the difference, which was noticed by Fey et al. [Phys. Rev. Lett. 104, 145703 (2010)PRLTAO0031-900710.1103/PhysRevLett.104.145703], between the steady state density of an Abelian sandpile model (ASM) and the transition point of its corresponding deterministic fixed-energy sandpile model (DFES). Being deterministic, the configuration space of a DFES can be divided into two disjoint classes such that every configuration in one class should evolve into one of absorbing states, whereas no configurations in the other class can reach an absorbing state. Since the two classes are separated in terms of toppling dynamics, the system can be made to exhibit an absorbing phase transition (APT) at various points that depend on the initial probability distribution of the configurations. Furthermore, we show that in general the transition point also depends on whether an infinite-size limit is taken before or after the infinite-time limit. To demonstrate, we numerically study the two-dimensional DFES with Bak-Tang-Wiesenfeld toppling rule (BTW-FES). We confirm that there are indeed many thresholds. Nonetheless, the critical phenomena at various transition points are found to be universal. We furthermore discuss a ...Continue Reading

References

Jul 27, 1987·Physical Review Letters·P BakK Wiesenfeld
Apr 2, 1990·Physical Review Letters·D Dhar
Nov 23, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·A VespignaniS Zapperi
Dec 12, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·R DickmanS Zapperi
Apr 24, 2002·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M A MuñozS Zapperi
Feb 21, 2006·Physical Review Letters·Luca Dall'Asta
May 21, 2010·Physical Review Letters·Anne FeyDavid B Wilson

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