  A quasi 2-dimensional recursive lattice formed by planar elements have been
designed to investigate the surface thermodynamics of Ising spin glass system
with the aim to study the metastability of supercooled liquids and the ideal
glass transition. The lattice is constructed as a hybrid of partial Husimi
lattice representing the bulk and 1D single bonds representing the surface. The
recursive properties of the lattices were adopted to achieve exact
calculations. The model has an anti-ferromagnetic interaction to give rise to
an ordered phase identified as crystal, and a metastable solution representing
the amorphous/metastable phase. Interactions between particles farther away
than the nearest neighbor distance are taken into consideration. Free energy
and entropy of the ideal crystal and supercooled liquid state of the model on
the surface are calculated by the partial partition function. By analyzing the
free energies and entropies of the crystal and supercooled liquid state, we are
able to identify the melting transition and the second order ideal glass
transition on the surface. The results show that due to the coordination number
change, the transition temperature on the surface decreases significantly
compared to the bulk system. Our calculation agrees with experimental and
simulation results on the thermodynamics of surfaces and thin films conducted
by others.
