Finite-size effects on the behavior of the susceptibility in van der Waals films under $+,+$ boundary conditions

TL;DR

This paper investigates how finite-size effects influence the susceptibility near critical points in van der Waals films with identical boundary preferences, providing specific predictions for helium films near their critical points.

Contribution

It offers a theoretical analysis of finite-size effects on susceptibility in van der Waals films with symmetric boundary conditions, including predictions for helium film behavior near criticality.

Findings

Predicted susceptibility behavior near critical points for helium films.

Analyzed effects of boundary conditions on phase transitions.

Provided theoretical framework for finite-size effects in van der Waals systems.

Abstract

We study critical point finite-size effects in the case of the susceptibility of a film in which interactions are characterized by a van der Waals-type power law tail. The geometry is appropriate to a slab-like system with two bounding surfaces. Boundary conditions are consistent with surfaces that both prefer the same phase in the low temperature, or broken symmetry, state. We take into account both interactions within the system and interactions between the constituents of the system and the material surrounding it. Specific predictions are made with respect to the behavior of a $^3$He and $^4$He films in the vicinity of their respective liquid-vapor critical points.