Europhys. Lett.
Volume 63, Number 4, August 2003
Page(s) 512 - 518
Section General
Published online 01 November 2003
DOI: 10.1209/epl/i2003-00561-8
Europhys. Lett., 63 (4) , pp. 512-518 (2003)

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

F. Bagnoli1, F. Cecconi2, A. Flammini3 and A. Vespignani4

1  Dipartimento di Energetica "S. Stecco" - Via S. Marta 3, I-50139 Firenze, Italy
2  INFM and Dipartimento di Fisica, Università di Roma "La Sapienza" P.le A. Moro 2, I-00185 Roma, Italy
3  INFM and International School for Advanced Studies (SISSA/ISAS) via Beirut 4, I-34014 Trieste, Italy
4  Laboratoire de Physique Théorique (UMR du CNRS 8627), Bâtiment 210 Université de Paris-Sud - 91405 Orsay Cedex, France

(Received 13 March 2003; accepted in final form 16 June 2003)

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 $\rho_{\ab{a}}$ (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 the $\zeta$- $\rho_{\ab{a}}$ phase diagram can be traced back to the basic symmetries underlying the model's dynamics.

05.70.Ln - Nonequilibrium and irreversible thermodynamics.
05.65.+b - Self-organized systems.
05.50.+q - Lattice theory and statistics (Ising, Potts, etc.).

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