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Non-trivial exponents in coarsening phenomena

Abstract : One of the simplest examples of stochastic automata is the Glauber dynamics of ferromagnetic spin models such as Ising or Potts models. At zero temperature, if the initial condition is random, one observes a pattern of growing domains with a characteristic size which increases with time like t12. In this self-similar regime, the fraction of spins which never flip up to time t decreases like t−θ where the exponent θ is non-trivial and depends both on the number q of states of the Potts model and on the dimension of space. This exponent can be calculated exactly in one dimension. Similar non-trivial exponents are also present in even simpler models of coarsening, where the dynamical rule is deterministic.
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https://hal.archives-ouvertes.fr/hal-03285617
Contributor : Bernard Derrida <>
Submitted on : Wednesday, July 21, 2021 - 9:39:39 AM
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B. Derrida. Non-trivial exponents in coarsening phenomena. Physica D: Nonlinear Phenomena, Elsevier, 1997, Lattice Dynamics, 103 (1-4), pp.466-477. ⟨10.1016/S0167-2789(96)00278-3⟩. ⟨hal-03285617⟩

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