Inherent structures enumeration for low-density materials

This paper examines the enumeration of potential energy minima (inherent structures) for attracting particles at number densities below rho (s), the ``shredding point{''} for amorphous deposits. In this low density regime, typical inherent structures are spatially nonuniform, consisting of dense regions penetrated by irregular void space. Two distinct arguments are advanced concluding independently that in this regime the number Omega (1)(N, V) of distinguishable inherent structures for N particles in volume V has an exponential rise rate with N, alpha(rho), that diverges as rho-->0. A third argument examines the infinite volume limit and concludes that the asymptotic N dependence of ln Omega (1)(N,infinity) is dominated by a term proportional to N ln N.