  The space fractional Cahn-Hilliard phase-field model is more adequate and
accurate in the description of the formation and phase change mechanism than
the classical Cahn-Hilliard model. In this article, we propose a temporal
second-order energy stable scheme for the space fractional Cahn-Hilliard model.
The scheme is based on the second-order backward differentiation formula in
time and a finite difference method in space. Energy stability and convergence
of the scheme are analyzed, and the optimal convergence orders in time and
space are illustrated numerically. Note that the coefficient matrix of the
scheme is a $2 \times 2$ block matrix with a Toeplitz-like structure in each
block. Combining the advantages of this special structure with a Krylov
subspace method, a preconditioning technique is designed to solve the system
efficiently. Numerical examples are reported to illustrate the performance of
the preconditioned iteration.
