  Efficient and unconditionally stable high order time marching schemes are
very important but not easy to construct for nonlinear phase dynamics. In this
paper, we propose and analysis an efficient stabilized linear Crank-Nicolson
scheme for the Cahn-Hilliard equation with provable unconditional stability. In
this scheme the nonlinear bulk force are treated explicitly with two
second-order linear stabilization terms. The semi-discretized equation is a
linear elliptic system with constant coefficients, thus robust and efficient
solution procedures are guaranteed. Rigorous error analysis show that, when the
time step-size is small enough, the scheme is second order accurate in time
with aprefactor controlled by some lower degree polynomial of $1/\varepsilon$.
Here $\varepsilon$ is the interface thickness parameter. Numerical results are
presented to verify the accuracy and efficiency of the scheme.
