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The Thermodynamic Behaviors and Glass Transition on the Surface/Thin Film of An Ising Spin Model on Recursive Lattice

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.