Crossover from attractive to repulsive Casimir forces and vice versa

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Surface Physics

Background:

• O(n) symmetrical varphi;{4} Hamiltonian systems are relevant in critical phenomena.
• Critical Casimir forces arise from boundary effects in confined systems near critical points.
• Understanding these forces is crucial for systems with specific boundary conditions.

Purpose of the Study:

• To investigate critical Casimir forces in a d-dimensional film geometry at bulk critical points.
• To analyze the dependence of these forces on film thickness (L) and boundary conditions.
• To determine the scaling form of the excess free energy and present explicit renormalization group results.

Main Methods:

• Consideration of O(n) symmetrical varphi;{4} Hamiltonian in d-dimensional film geometry.
• Analysis of symmetry-preserving boundary conditions of the form partial differential_{n}phi=c[over composite function]_{j}phi.
• Application of two-loop renormalization group techniques to derive results at d=4- dimensions.

Main Results:

• The L-dependent part of the reduced excess free energy follows a scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} for d<4.
• The Casimir force can be either attractive or repulsive, contingent upon the scaling fields c_{1} and c_{2}.
• Crossovers between attraction and repulsion (and vice versa) are observed as film thickness L increases, for specific boundary condition enhancements.

Conclusions:

• The critical Casimir force in these systems is tunable via boundary conditions and film thickness.
• The study provides explicit quantitative predictions for the Casimir force behavior using renormalization group methods.
• These findings have implications for understanding interfacial phenomena in systems near criticality.