Absence of the link between self-organized criticality and deterministic fixed energy sandpiles

Details Absence of the link between self-organized criticality and deterministic fixed energy sandpiles Absence of the link between self-organized criticality and deterministic fixed energy sandpiles

2010-01-19

arxiv.org/abs/1001.3359v1

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

Self-organized criticality (SOC) observed in an abelian sandpile model (ASM) has been believed to be related to the absorbing phase transitions (APT) exhibited by a deterministic fixed energy sandpile (DFES). We critically investigate the link between the SOC and the APT exhibited by the DFES. In contrast to the widespread belief, a phase transition in the DFES is shown not to be defined uniquely but to depend on initial conditions because of the non-ergodicity of the DFES. Furthermore, we show that a phase transition in the spreading dynamics of the DFES is intimately related to the percolation rather than the avalanche dynamics of the ASM. These results illustrate that the SOC exhibited by the ASM has nothing to do with phase transitions in the DFES. We discuss the implication of our result to stochastic models.

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