Regensburg 2007 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 30: Poster II
DY 30.28: Poster
Donnerstag, 29. März 2007, 16:00–18:00, Poster D
Excess free energy and Casimir forces in slabs with periodic boundary conditions at and above the bulk critical temperature — •Daniel Grüneberg and Hans Werner Diehl — Universität Duisburg-Essen (Campus Duisburg), Fachbereich Physik, D-47048 Duisburg, Germany
We consider systems that are describable by n-component short-range φ4 models in a ∞d−1× L slab geometry of finite thickness L with periodic boundary conditions along the finite dimension. Within these models the excess free energy and the thermodynamic Casimir force are evaluated at and above the bulk critical temperature Tc,∞
using the renormalization-group improved perturbation theory in d=4−є dimensions. This theory has recently been re-examined in Ref. [1], and is found to be ill-defined beyond two-loop order when the boundary conditions (bc) are such that the free propagator involves a zero-energy mode. This applies to periodic bc and special-special ones, and leads to a non-analyticity of the free energy for L<∞ at the bulk critical point (bcp). The remedy is a reorganization of the field theory with regard to a proper treatment of the zero-energy mode [1]. This reorganized field theory is employed to derive the finite-size scaling functions of the excess free energy and the Casimir force. Their values at the bcp are related to the critical Casimir amplitude Δper, whose small-є expansion is found to involve—besides integers powers of є—fractional powers єk/2 with k≥3, and powers of logє. We present explicit results for Δper to order є3/2, which are used to estimate its value at d=3.
[1] H. W. Diehl et al., Europhys. Lett. 75, 241 (2006)