Ran Huang, Purushottam D. Gujrati
Two kinds of recursive lattices having the same coordination number but different unit cells (2-D square and 3-D cubic cells) are constructed and an antiferromagnetic Ising model is solved exactly on them to study stable and metastable states. The Ising model with multi-particle interactions is designed to represent a monatomic system or an alloy and exhibits the phenomenon of supercooled liquid and the ideal glass transition. Based on the solutions, the thermodynamics on both lattices was examined. In particular, the free energy, energy and entropy of the ideal glass, supercooled liquid, crystal and liquid state of the model on each lattice were calculated and compared. Interactions between particles farther away than the nearest neighbor distance are taken into consideration. The two lattices allow us to compare the effects of the unit cells on thermodynamics and to indicate the advantages and disadvantages of each lattice.
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http://arxiv.org/abs/1209.2090
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