Standard Mean-field Theory Research Articles

The Curie temperature of thin films; the role of anisotropy at the surfaces

The ferromagnetic phase transition in thin films consisting of spin- 1 2 Ising layers with spin- 3 2 overlayers is studied by the use of the effective-field theory superior to the standard mean-field theory. The model calculation shows that the Curie temperature severely depends on the value of the single-ion anisotropy D at the surfaces, namely inplane ( D < 0) or perpendicular ( D > 0), as well as the thickness and the interactions at and with the surfaces.

Ferrimagnetism in a disordered binary alloy

The magnetic properties (transition temperature, compensation temperature and magnetizations) of a disordered ferrimagnetic binary alloy are studied by the use of two theoretical frameworks, namely the standard mean-field theory and the effective-field theory with correlations. The authors' find a number of outstanding phenomena in ferrimagnetism, such as the possibility of many compensation points in the total magnetization curve and magnetization curves not predicted in the Neel theory.

Density-functional theory of the water liquid-vapour interface

An extended mean-field density-functional theory of the liquid-vapour interface of water is described. The theory generalizes standard mean-field theories of inhomogeneous molecular fluids by including quadratic orders of the anisotropic component of the intermolecular pair potential in the free energy functional. The pair interaction is modelled by an isotropic plus point dipolar and quadrupolar potential. Analysis shows that dipole-quadrupole coupling terms in the potential are responsible for inducing spontaneous polarization at the liquid-vapour interface. The direction of the surface polarization is determined by the sign of the axial component of the molecular quadrupole tensor, as in the earlier phenomenological theory of Stillinger and Ben-Naim. Explicit calculations are performed using molecular interaction parameters given by the TIP4P potential model for water, employed in recent computer simulations of the water interface by Wilson, Pohorille and Pratt. The preferred molecular orientations at the interface predicted by the theory are analysed in detail and compared with previous simulation results.

A comparative study of standard and non-standard mean-field theories for the energy, the first and the second moments of Be and LiH

Many-body perturbation theory (MBPT) based on Hartree-Fock and non-standard mean fields is employed to calculate the energy, the first and the second moments of Be and LiH. The results are compared with the 'exact' energy, etc obtained in a finite-dimensional model Hilbert space (full configuration interaction taken into account). The authors test the idea that part of the correlations calculated in a Hartree-Fock MBPT scheme can be simulated as mean field or low-order effects when non-standard mean fields derived in non-relativistic or relativistic quantum electrodynamics with non-standard gauges are employed to set up a systematic perturbation theory.

Comparison of effective-field and mean-field theories for the spin-one Ising model with a random crystal field

The phase diagram of the spin-one Ising model with a random crystal field is investigated by the use of the effective-field theory with correlations. The important differences from the results obtained by the standard mean-field theory are indicated. The differences are very similar to those found in the dilution problem of magnetic systems.

Self-consistent normal ordering of gauge field theories

Mean field theories with a real action of unconstrained fields can be self-consistently normal ordered. This leads to a considerable improvement over standard mean-field theory. This concept is applied to lattice gauge theories. We construct first an appropriate real action mean-field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean-field theory are derived.

Mean fields and self consistent normal ordering of lattice spin and gauge field theories

Classical Heisenberg spin models on lattices possess mean field theories that are well defined real field theories on finite lattices. These mean field theories can be self consistently normal ordered. This leads to a considerable improvement over standard mean field theory. This concept is carried over to lattice gauge theories. We construct first an appropriate real mean field theory. The equations determining the Gaussian kernel necessary for self-consistent normal ordering of this mean field theory are derived.