The self-consistent Ornstein-Zernike approach (SCOZA) developed earlier by the authors for the lattice gas and Ising model as well as simple continuum fluids is extended to the D-vector spin model that includes the classical rotator model (D = 2), the classical Heisenberg model (D = 3), and the...

An Ornstein–Zernike approximation for the two-body correlation function embodying thermodynamic consistency is applied to a system of classical Heisenberg spins on a three-dimensional lattice. The consistency condition determined in a previous work is supplemented by introducing a simplified...

The development of a general theory of clustering is sketched. The primary focus is on the use of the pair connectedness function in problems of correlated clustering and on the Ornstein-Zernike formalism that has been developed to evaluate this function and relate it to observed mesoscopic and...

The origin of the tricritical point (tcp) in ionic solutions and its dependence on the short-range effective free energies (SR) are studied within a Landau–Ginzburg–Wilson approach. The tcp is associated with a continuous transition to a charge-ordered phase, in which the charge density...

Some properties of the Boltzmann equation (BE) for a spatially uniform system of Maxwellian molecules are considered, including the explicit evaluation of the energy-space transition probability P(y, z; x), the evaluation of the constants λn and μn,i which enter in the moment equations, the...

Standard statistical mechanical approximations (e.g. mean-field approximations) for pair-correlation functions of strongly interacting systems that yield adequate thermodynamics away from critical points typically break down badly in critical regions. The self-consistent Ornstein–Zernike...

The Van der Waals force (or Casimir force) between two semi-infinite dielectric slabs – conventionally derived via field theoretical methods – is derived in a novel way using the quantum statistical mechanical model introduced earlier by Høye–Stell and others. Both the static case, and...

A statistical mechanical explanation of the freezing transition which is exact in a certain limit, is worked out.

We consider the two-dimensional Coulomb gas. To avoid the well-known collapse of the system below a certain temperature the Coulomb interaction is cut inside a core radius. In our statistical mechanical treatment we are able to formally describe the idea that oppositly charged ions tend to...

We study time dependent correlation functions of ideal classical and quantum gases using methods of equilibrium statistical mechanics. The basis for this is the path integral formalism of quantum mechanical systems. By this approach the statistical mechanics of a quantum mechanical system...