  We investigate the multi-order parameter phase field model of Steinbach and
Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase
transformations using interface fields, Physica D 134 (1999) 385-393]
concerning its ability to describe grain boundary premelting. For a single
order parameter situation solid-melt interfaces are always attractive, which
allows to have (unstable) equilibrium solid-melt-solid coexistence above the
bulk melting point. The temperature dependent melt layer thickness and the
disjoining potential, which describe the interface interaction, are affected by
the choice of the thermal coupling function and the measure to define the
amount of the liquid phase. Due to the strictly finite interface thickness also
the interaction range is finite. For a multi-order parameter model we find
either purely attractive or purely repulsive finite-ranged interactions. The
premelting transition is then directly linked to the ratio of the grain
boundary and solid-melt interfacial energy.
