Critical free energy and Casimir forces in rectangular geometries

Abstract

We study the critical behavior of the free energy and the thermodynamic Casimir force in a $L_\parallel^{d-1} \times L$ block geometry in $2 1$), and zero for a cube $(ρ=1)$. We also present extrapolations to the cylinder limit ($ρ=\infty$) and to the film limit ($ρ=0$) for $n=1$ and $d=3$. Our analytic results for finite-size scaling functions in the minimal renormalization scheme at fixed dimension $d=3$ agree well with Monte Carlo data for the three-dimensional Ising model by Hasenbusch for $ρ=1$ and by Vasilyev et al. for $ρ=1/6$ above, at, and below $T_c$.