  The surface energy of the nucleus of a stable phase growing in the presence
of several amorphous metastable phases of character intermediate between the
initial and the final phases may depend non-trivially on the size of the
nucleus. This size dependence is being increasingly used to explain diverse
non-equilibrium phase selection, and relaxation, as in the random first-order
transition (RFOT) theory of glasses. Here we develop an order parameter based
Ginzburg-Landau approach that explicitly includes the rugged free energy
landscape due to the metastable phases. The fractional dependence of total
surface energy between melt and stable solid phase on the number of metastable
phases($N_{MS}$) has been interrogated in this study. We have also analyzed how
this fractional dependence gets modified with temperature. We find that the
fractional size dependence of surface energy is omnipresent, arises from the
minimization of free energy and demands certain ordering of metastable phases
in the interface. Our results could recover the celebrated result of Villain
that forms the basis of RFOT theory of glasses. We find the additional result
that the surface tension saturates to a finite size independent value.
