Critical Casimir force in slab geometry with finite aspect ratio: Analytic calculation above and belowV. 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 slab geometry with a finite aspect ratio above, at, and below on the basis of the O(n) symmetric isotropic 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 1/4. Our analytic result for the Casimir force scaling function for = 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 .
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.
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