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The Steady State Of The Tapped Ising Model

Author

Listed:
  • DAVID S. DEAN

    (IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France)

  • ALEXANDRE LEFEVRE

    (IRSAMC, Laboratoire de Physique Quantique, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 04, France)

Abstract

We consider a tapping dynamics, analogous to that in experiments on granular media, on the simple one-dimensional ferromagnetic Ising model. When unperturbed, the system undergoes a single spin flip falling dynamics where only energy lowering moves occur. With this dynamics the system has an exponentially large number of metastable states and gets stuck in blocked or jammed configurations as do granular media. When stuck, the system is tapped, in order to make it evolve, by flipping in parallel each spin with probabilityp(corresponding to the strength of the tapping). Under this dynamics the system reaches a steady state regime characterized by an asymptotic energy per spinE(p), which is determined analytically. Within the steady state regime we compare certain time averaged quantities with the ensemble average of Edwards based on a canonical measure over metastable states of fixed average energy. The ensemble average yields results in excellent agreement with the dynamical measurements.

Suggested Citation

  • David S. Dean & Alexandre Lefevre, 2001. "The Steady State Of The Tapped Ising Model," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 4(04), pages 333-343.
    • Handle: RePEc:wsi:acsxxx:v:04:y:2001:i:04:n:s0219525901000255
    DOI: 10.1142/S0219525901000255
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