Another method to compute the thermodynamic Casimir force in lattice models

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Computational Physics

Background:

• The Casimir effect describes a quantum mechanical force arising from vacuum fluctuations.
• Calculating the thermodynamic Casimir force in lattice models often requires complex numerical methods.
• Previous methods involved integrating energy densities, which can be computationally intensive.

Purpose of the Study:

• To present a more efficient method for computing the thermodynamic Casimir force in lattice models.
• To validate the new method using a well-studied system, the XY universality class.
• To enable single Monte Carlo simulations for thermodynamic Casimir force calculations.

Main Methods:

• A novel Monte Carlo simulation technique is proposed.
• The method is analogous to approaches used for 't Hooft loops and interface tension in SU(N) lattice gauge models.
• The improved two-component phi4 model on a simple cubic lattice is simulated.

Main Results:

• The thermodynamic Casimir force can be computed at a given temperature using a single simulation.
• The method was successfully tested on thin films within the XY universality class.
• Results are comparable to those obtained through numerical integration of energy densities.

Conclusions:

• The developed method offers a computationally efficient alternative for determining the thermodynamic Casimir force.
• This technique simplifies the study of Casimir forces in various lattice models.
• The findings contribute to a better understanding of critical phenomena and finite-temperature effects in physical systems.