Transitions in non-conserving models of Self-Organized Criticality

Details Transitions in non-conserving models of Self-Organized Criticality Transitions in non-conserving models of Self-Organized Criticality

1995-10-23

arxiv.org/abs/cond-mat/9510130v1

Physics

Condensed Matter

8 pages in latex format; 5 figures available upon request

Scientific paper

10.1103/PhysRevLett.76.2326

We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, $\alpha_c$, is approached, the cut--off of the avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The transition from non-SOC to SOC behaviour is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system. The relevance of the results are discussed in connection to the nearest-neighbours OFC model (in particular we analyse the relevance of synchronization in the latter).

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