Critical Casimir force in slab geometry with finite aspect ratio: Analytic calculation above and below Tc

V. Dohm

doi:10.1209/0295-5075/86/20001

All issues

Volume 86 / No 2 (April 2009)

EPL, 86 2 (2009) 20001

Abstract

Issue		EPL Volume 86, Number 2, April 2009


Article Number		20001
Number of page(s)		5
Section		General
DOI		https://doi.org/10.1209/0295-5075/86/20001
Published online		24 April 2009

EPL, 86 (2009) 20001

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

V. Dohm

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

Corresponding author: vdohm@physik.rwth-aachen.de

Received: 18 February 2009
Accepted: 20 March 2009

Abstract

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 ρ = 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 $T_{{\rm c}}$ .

PACS: 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

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