Ising model with memory: coarsening and persistence properties

Fabio Caccioli 1, 2, Silvio Franz 3, Matteo Marsili 4

Journal of Statistical Mechanics: Theory and Experiment (2008) 07006

We consider the coarsening properties of a kinetic Ising model with a memory field. The probability of a spin-flip depends on the persistence time of the spin in a state. The more a spin has been in a given state, the less the spin-flip probability is. We numerically studied the growth and persistence properties of such a system on a two dimensional square lattice. The memory introduces energy barriers which freeze the system at zero temperature. At finite temperature we can observe an apparent arrest of coarsening for low temperature and long memory length. However, since the energy barriers introduced by memory are due to local effects, there exists a timescale on which coarsening takes place as for the Ising model. Moreover the two point correlation functions of the Ising model with and without memory are the same, indicating that they belong to the same universality class.

  • 1. international school for advenced stydy,
    international school
  • 2. Istituto Nazionale di Fisica Nucleare,
    Istituto Nazionale di Fisica Nucleare
  • 3. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 4. The Abdus Salam International Centre for Theoretical Physics,
    ICTP Trieste