Casimir force in the rotor model with twisted boundary conditions

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics

Background:

• Investigating the three-dimensional lattice XY model with nearest neighbor interaction.
• The system features a vector order parameter on a cubic lattice within a film geometry.

Purpose of the Study:

• To study the mean length and orientation of the vector order parameter.
• To analyze the Casimir force generated by the system.
• To understand the influence of temperature (T), boundary angle (α), and film thickness (L).

Main Methods:

• Utilizing the mean field approximation.
• Analyzing the system's behavior as a function of temperature, boundary angle, and thickness.

Main Results:

• The Casimir force exhibits continuous dependence on α and T, and can be attractive or repulsive.
• Both the sign and magnitude of the Casimir force are reversibly controlled by varying α and/or T.
• An additional phase transition, unique to finite systems, is discovered for α=π, linked to vector orientation variations.

Conclusions:

• The mean field approximation provides insights into controllable Casimir forces in confined systems.
• The discovered phase transition in finite systems offers new avenues for research in statistical mechanics.
• This work demonstrates a tunable mechanism for generating attractive or repulsive Casimir forces.