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Hysteresis and return-point memory in deterministic cellular automata

Physical Review Letters
American Physical Society
Publication Date
  • Histèresi
  • Transformacions De Fase (Física Estadística)
  • Materials Magnètics
  • Hysteresis
  • Phase Transformations (Statistical Physics)
  • Magnetic Materials


We have investigated hysteresis and the return-point memory (RPM) property in deterministic cellular automata with avalanche dynamics. The RPM property reflects a partial ordering of metastable states, preserved by the dynamics. Recently, Sethna et al. [Phys. Rev. Lett. 70, 3347 (1993)] proved this behavior for a homogeneously driven system with static disorder. This Letter shows that the partial ordering and the RPM can be displayed as well by systems driven heterogeneously, as a result of its own evolution dynamics. In particular, we prove the RPM property for a deterministic 2D sandpile automaton driven at a central site.

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