Charles Radin and Lorenzo Sadun
A mean field analysis of the fluid/solid phase transition
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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.