NONTRIVIAL EXPONENTS IN COARSENING PHENOMENA

One of the simplest examples of stochastic automata is the Glauber dyn amics of ferromagnetic spin models such as Ising or Ports models. At z ero temperature, if the initial condition is random, one observes a pa ttern of growing domains with a characteristic size which increases wi th time like t(1/2). In this self-similar regime, the fraction of spin s which never flip up to time t decreases like r(-theta) where the exp onent 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 ar e also present in even simpler models of coarsening, where the dynamic al rule is deterministic.