<p>This manuscript focuses on a class of second order numerical schemes for certain phase field models. It is known that phase field models are gradient flows therefore the energy dissipates in time. As a matter of fact, numerical simulations with unconditional energy stability (energy decays in time regardless of the size of the time step) indicate good stability. Recently several first order semi-implicit schemes for the Allen-Cahn and Cahn-Hilliard equations were developed satisfying the energy-decay property. In this paper the analysis will be extended to second order schemes for the two dimensional Allen-Cahn equation with a rigorous proof of energy stability.</p>