  Implicit-Explicit methods have been widely used for the efficient numerical
simulation of phase field problems such as the Cahn-Hilliard equation or thin
film type equations. Due to the lack of maximum principle and stiffness caused
by the effect of small dissipation coefficient, most existing theoretical
analysis relies on adding additional stabilization terms, mollifying the
nonlinearity or introducing auxiliary variables which implicitly either changes
the structure of the problem or trades accuracy for stability in a subtle way.
In this work we introduce a robust theoretical framework to analyze directly
the stability of the standard implicit-explicit approach without stabilization
or any other modification. We take
  the Cahn-Hilliard equation as a model case and prove energy stability under
natural time step constraints which are optimal with respect to energy scaling.
These settle several questions which have been open since the work of Chen and
Shen \cite{CS98}.
