Aspect-ratio dependence of thermodynamic Casimir forces

Understand

We consider the three-dimensional Ising model in a $L_\perp \times L_\parallel \times L_\parallel$ cuboid geometry with finite aspect ratio $\rho = L_\perp/L_\parallel$ and periodic boundary conditions along all directions.

• For this model the finite-size scaling functions of the excess free energy and thermodynamic Casimir force are evaluated numerically by means of Monte Carlo simulations.
• The Monte Carlo results compare well with recent field theoretical results for the Ising universality class at temperatures above and slightly below the bulk critical temperature $T_\mathrm{c}$.
• Furthermore, the excess free energy and Casimir force scaling functions of the two-dimensional Ising model are calculated exactly for arbitrary $\rho$ and compared to the three-dimensional case.