Complexity calculation for an amorphous metastable solid

We use a field-theoretic model to study the partition function of a many-particle system without quenched-disorder. The model is formulated in terms of the coarse-grained density field ρ ( x ) used in classical density functional theory (DFT). A corresponding free energy landscape (FEL) is depicted in the function space of the continuum field. The number of local minima in the FEL is defined as the Complexity S c . Following the standard trick of mapping into a composite system of m identical replicas, and finally taking the m → 1 limit, S c is calculated. The two-point structural correlations of the density fluctuations are needed as an input. A vital step of the present work is using the static correlations of the inhomogeneous metastable state obtained in classical DFT. The inhomogeneous state is described in terms of overlapping Gaussian density profiles centred on a set of random lattice points { R i } . Our results for S c ( η ) on extrapolation to higher packing fractions ( η )tends to zero, obtaining the corresponding Kauzmann point η K . We obtain the dependence of the η K on the properties of the inhomogeneous structure for the structure { R i } .