Off-critical Casimir effect in Ising Slabs with Symmetric Boundary Conditions in d=3

TL;DR

This paper investigates the off-critical Casimir effect in three-dimensional Ising slabs with symmetric boundary conditions using the extended de Gennes-Fisher local-functional method, providing universal scaling functions and asymptotic behaviors.

Contribution

It applies the EdGF local-functional method to analyze the off-critical Casimir effect in 3D Ising systems, deriving universal scaling functions and their asymptotic behaviors.

Findings

Universal scaling functions for Casimir force and Gibbs adsorption are obtained.

Asymptotic behavior of the Casimir force scaling function is analyzed in general dimensions.

A mean-field form of the Gibbs adsorption scaling function is derived.

Abstract

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 $d$.