Inherent structures enumeration for low-density materials - art. no. 011110

This paper examines the enumeration of potential energy minima (inherent st ructures) for attracting particles at number densities below rho (s), the " shredding point" for amorphous deposits. In this low density regime, typica l inherent structures are spatially nonuniform, consisting of dense regions penetrated by irregular void space. Two distinct arguments are advanced co ncluding independently that in this regime the number Omega (1)(N, V) of di stinguishable inherent structures for N particles in volume V has an expone ntial rise rate with N, alpha(rho), that diverges as rho-->0. A third argum ent 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.