  A symmetric phase field model is used to study wavelength selection in two
dimensions. We study the problem in a finite system using a two-pronged
approach. First we construct an action and, minimizing this, we obtain the most
probable configuration of the system, which we identify with the selected
stationary state. The minimization is constrained by the stationary solutions
of stochastic evolution equations and is done numerically. Secondly, additional
support for this selected state is obtained from straightforward simulations of
the dynamics from a variety of initial states.
