  In this work we develop a stochastic algorithm to integrate the Cahn-Hilliard
equations. The algorithm is based on Gillespie's stochastic simulation
algorithm, also known as kinetic Monte Carlo. The deterministic integration of
the phase field equations leads to the closest minimum of free energy and does
not overcome free energy barriers. However, in the nucleation and growth regime
of the phase diagram, free energy barriers need to be thermally overcome for
the system to phase separate to reach equilibrium. We show in this work that
the proposed stochastic integration algorithm indeed allows the system to
overcome free energy barriers. We discuss the results in terms of fluctuation
distributions, grid sizes and efficiency.
