  We derive a posteriori error estimates for a fully discrete finite element
approximation of the stochastic Cahn-Hilliard equation. The a posteriori bound
is obtained by a splitting of the equation into a linear stochastic partial
differential equation (SPDE) and a nonlinear random partial differential
equation (RPDE). The resulting estimate is robust with respect to the
interfacial width parameter and is computable since it involves the discrete
principal eigenvalue of a linearized (stochastic) Cahn-Hilliard operator.
Furthermore, the estimate is robust with respect to topological changes as well
as the intensity of the stochastic noise. We provide numerical simulations to
demonstrate the practicability of the proposed adaptive algorithm.
