  I consider a physical system described by a continuous field theory and
enclosed in a large but finite cubical box with periodic boundary conditions.
The system is assumed to undergo a continuous phase transition at some critical
point. The \phi^4 theory that is a continuous version of the Ising model is
such a system but there are many other examples corresponding to higher spin,
higher symmetry etc. The eigenfunctions of the corresponding Fokker-Planck
operator can be chosen, of course, to be eigenfunctions of the momentum
operator. It is shown that the eigenvalues of the FP operator, corresponding to
each eigenvalue q of the momentum operator, evaluated at a transition point of
the finite system, accumulate at zero, when the size of the system tends to
infinity. There are many reasonable ways of defining a critical temperature of
a finite system, that tends to the critical temperature of the infinite system
as the size of the system tends to infinity. The accumulation of eigenvalues is
neither affected by the specific choice of critical temperature of the finite
system nor by whether the system is below or above its upper critical
dimension.
