Non-trivial exponents in coarsening phenomena

[摘要] One of the simplest examples of stochastic automata is the Glauber dynamics of ferromagnetic spin models such as Ising or Ports 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 t(1/2). In this self-similar regime, the fraction of spins which never flip up to time t decreases like r(-theta) where the exponent theta is non-trivial and depends both on the number q of stares of the Potts model and an 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.

[发布日期] 1997-04-15

[效力级别]  Proceedings Paper