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 rho(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 Sc. Following the standard trick of mapping into a composite system of m identical replicas, and finally taking the m -> 1 limit, Sc 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 {Ri}. Our results for Sc(eta) on extrapolation to higher packing fractions (eta)tends to zero, obtaining the corresponding Kauzmann point eta K. We obtain the dependence of the eta K on the properties of the inhomogeneous structure for the structure {Ri}.

Automated summary

We use a field-theoretic model to study the partition function of a many-particle system without quenched -disorder. A corresponding free energy landscape (FEL) is depicted in the function space of the continuum field, and the number of local minima in the FEL, defined as the Complexity Sc, is calculated. The study shows the dependence of the Kauzmann point on the properties of the inhomogeneous structure.