Critical energy-density profile near walls.

We examine critical adsorption for semi-infinite thermodynamic systems of the Ising universality class when they are in contact with a wall of the so-called normal surface universality class in spatial dimension d=3 and in the mean-field limit. We apply local-functional theory and Monte Carlo simulations in order to quantitatively determine the properties of the energy density as the primary scaling density characterizing the critical behaviors of Ising systems besides the order parameter. Our results apply to the critical isochore, near two-phase coexistence, and along the critical isotherm if the surface and the weak bulk magnetic fields are either collinear or anticollinear.

Crossover aspects in Ising strips under the influence of variable surface fields and a grain boundary.

I use an exact variational formulation of Mikheev and Fisher to study the critical Ising strip with a grain boundary and confining surfaces characterized by arbitrary and different surface magnetic fields. Energy density profiles that serve as order parameters of the system within the used method show strong nonmonotonous behavior in the vicinity of confining surfaces. I consider short-distance expansion of energy density profiles.

Off-critical Casimir effect in Ising slabs with symmetric boundary conditions in d=3.

Extended de Gennes-Fisher (EdGF) local-functional method has been applied to the thermodynamic Casimir effect away from the critical point for systems in the Ising universality class confined between parallel plane plates with symmetric boundary conditions [denoted (ab)=(++)]. Results on the universal scaling functions of the Casimir force W++(y) (y is a temperature-dependent scaling variable) and Gibbs adsorption G[over ](y) are presented in spatial dimension d=3. Also, the mean-field form of the universal scaling function of the Gibbs adsorption G[over ](y) is derived within the local functional theory.

Local-functional theory of critical adsorption.

Local-functional methods are applied to critical adsorption in three-dimensional Ising-like systems. The universal order-parameter-profile scaling functions, P(+/-)(x), along the critical isochore (+) and phase boundary (-), are calculated along with their associated universal amplitudes. Good agreement is found with the results of Monte Carlo simulations.