Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

Details Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model Short period attractors and non-ergodic behavior in the deterministic fixed energy sandpile model

2002-07-29

arxiv.org/abs/cond-mat/0207674v2

Europhys. Lett. vol.63, pp.512-518 (2003)

Physics

Condensed Matter

Statistical Mechanics

EPL-style, 7 pages, 3 eps figures, revised version

Scientific paper

10.1209/epl/i2003-00561-8

We study the asymptotic behaviour of the Bak, Tang, Wiesenfeld sandpile automata as a closed system with fixed energy. We explore the full range of energies characterizing the active phase. The model exhibits strong non-ergodic features by settling into limit-cycles whose period depends on the energy and initial conditions. The asymptotic activity $\rho_a$ (topplings density) shows, as a function of energy density $\zeta$, a devil's staircase behaviour defining a symmetric energy interval-set over which also the period lengths remain constant. The properties of $\zeta$-$\rho_a$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.

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