Su-Chan Park (Catholic Univ.)
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). In this talk, I will illustrate that in contrast to the widespread belief, a phase transition in the DFES is not defined uniquely but to depend on initial conditions because of the non-ergodicity of the DFES. Furthermore, I will 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. The implication of our result to stochastic models will be discussed.