Volume 86, Number 2, April 2009
Article Number 20001
Number of page(s) 5
Section General
Published online 24 April 2009
EPL, 86 (2009) 20001
DOI: 10.1209/0295-5075/86/20001

Critical Casimir force in slab geometry with finite aspect ratio: Analytic calculation above and below $T_{\rm c}$

V. Dohm

Institute for Theoretical Physics, RWTH Aachen University - D-52056 Aachen, Germany, EU

received 18 February 2009; accepted in final form 20 March 2009; published April 2009
published online 24 April 2009

We study the critical Casimir force 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 $T_{\rm c}$ on the basis of the O(n) symmetric isotropic $\varphi^{4}$ field theory with short-range interactions. Exact results are obtained in the large-n limit. For n = 1, 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 $T_{\rm c}$.

05.70.Jk - Critical point phenomena.
64.60.-i - General studies of phase transitions.
75.40.-s - Critical-point effects, specific heats, short-range order.

© EPLA 2009