12-158 Charles Radin and Lorenzo Sadun

A mean field analysis of the fluid/solid phase transition (211K, pdf) Dec 28, 12

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Abstract. We study the fluid/solid phase transition via a mean field model using the language of large dense random graphs. We show that the entropy density, for fixed particle and energy densities, is minus the minimum of the large deviation rate function for graphs with independent edges. We explicitly compute this minimum for small energy density and a range of particle density, and show that the resulting entropy density must lose its analyticity at some point. This implies the existence of a phase transition, associated with the heterogeneous structure of the energy ground states.

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