Spectral derivation of the ornstein-zernike decay for four-point functions

Analytic solution of the Ornstein-Zernike relation for inhomogeneous liquids.

The properties of a classical simple liquid are strongly affected by the application of an external potential that supports inhomogeneity. To understand the nature of these property changes, the equilibrium particle distribution functions of the liquid have, typically, been calculated directly using either integral equation or density functional based analyses. In this study, we develop a diffe...

Self-consistent Ornstein-Zernike approximation for the Sogami-Ise fluid.

We generalize the self-consistent Ornstein-Zernike approximation (SCOZA) to a fluid of particles with a pair potential consisting of a hard-core repulsion and a linear combination of Sogami-Ise tails, w(r)=-epsilonsigma summation operator (nu)(K(nu)/r+L(nu)z(nu))e(-z(nu)(r-sigma)). The formulation and implementation of the SCOZA takes advantage of the availability of semianalytic results for su...

Multilevel wavelet solver for the Ornstein-Zernike equation

A multilevel wavelet algorithm is developed to solve integral equations for the pair correlations in simple liquids. The algorithm is based on the discrete wavelet transform of the radial correlation functions. The fundamental properties of wavelet bases are employed to improve the convergence and speed of the algorithm. The Coifman 2 basis set is used for the wavelet treatment. To solve the Or...

Ornstein-zernike Theory for the Finite Range Ising

Convergence of Density Expansions of Correlation Functions and the Ornstein-zernike Equation

Abstract. We prove convergence of the multi-body correlation function as a power series in the density. We work in the context of the cluster expansion in the canonical ensemble and we obtain bounds uniform in the volume and the number of particles. In the thermodynamic limit, the coefficients are characterized by sums over some class of two-connected graphs. We introduce the “direct correlatio...