Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$

TL;DR

This paper analytically investigates the critical Casimir force in a three-dimensional Ising model slab geometry with finite aspect ratio, providing results that align well with recent Monte Carlo simulations across different temperature regimes.

Contribution

It offers a new analytic calculation of the Casimir force scaling function for finite aspect ratios, extending understanding above, at, and below the critical temperature.

Findings

Analytic Casimir force scaling function agrees with Monte Carlo data.

Dependence of the force on aspect ratio is characterized for $ ho oughly 1/4$.

Results apply to slab geometries with periodic boundary conditions.

Abstract

We present a field-theoretic study of the critical Casimir force of the Ising universality class in a $d$-dimensional ${L_\parallel^{d-1} \times L}$ slab geometry with a finite aspect ratio $\rho = L/L_\parallel$ above, at, and below $T_c$. The result of a perturbation approach at fixed dimension $d=3$ is presented that describes the dependence on the aspect ratio in the range $\rho \gtrsim 1/4$. Our analytic result for the Casimir force scaling function for $\rho = 1/4$ agrees well with recent Monte Carlo data for the three-dimensional Ising model in slab geometry with periodic boundary conditions above, at, and below $T_c$.