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 {\it 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-dependant scaling variable) and Gibbs adsorption \(\tilde G(y)\) are presented in spatial dimension \(d=3\). Also, the mean-field form of the universal scaling function of the Gibbs adsorption \(\tilde G(y)\) is derived within the local functional theory. Asymptotic behavior of \(W_{++}(y)\) for very large values of the scaling variable \(y\) is analyzed in {\it general} dimension \(d\).