Non-universal critical Casimir force in confined near the superfluid transition

Abstract

We present the results of a one-loop calculation of the effect of a van der Waals type interaction potential ∼ |x| −d−σ on the critical Casimir force and specific heat of confined 4 He near the superfluid transition. We consider a 4 He film of thickness L. In the region L ξ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of O(ξ 2 L −d−σ ) to the critical temperature dependence of the Casimir force above T λ that dominates the universal scaling contribution ∼ e −L/ξ predicted by earlier theories. For the specific heat we find subleading non-scaling contributions of O(L −1 ) and O(L −d−σ ).

Diversity of critical behavior within a universality class

“…It was pointed out by Dantchev and Rudnick [15] that it affects the finite-size susceptibility in the regime L/ξ + ≫ 1, similar to the effect caused by a sharp cutoff [9]. The effect of this interaction on the excess free energy f ex s and on the critical Casimir force in the case of film geometry was first studied by Chen and the present author [11,18]. The asymptotic structure for L/ξ + ≫ 1 in one-loop order above T c at h = 0 is f ex s (t, L) = L −d F ex (L/ξ + ) + bL 2−σ Ψ(L/ξ + ) .…”

“…In Sects. III and X we shall consider the model (2.7) also in a fully isotropic form with the short-range interaction δ K(k) = k 2 including a finite cutoff Λ and, for n = 1, with the subleading long-range interaction [11,14,15,16,17,18,50,52]…”

“…e Refs. [11,14,15,16,17,18] ing functions. All of these nonuniversal differences exist in the asymptotic critical region |t| ≪ 1, L ≫ ã, and r ≫ ã where corrections to scaling in the sense of Wegner [19] are negligible.…”

“…1 . In the isotropic case, this region is of physical relevance for fluids with van der Waals interactions [11,14,15,16,17,18,50,52].…”

Excess free energy and Casimir forces in systems with long-range interactions of van der Waals type: General considerations and exact spherical-model results

“…When T ≃ T c,∞ , they compete with the long-ranged Casimir force produced by critical or near-critical fluctuations. As previous work [36][37][38][39]44] suggests, and will be shown in detail below, they actually become the dominant part of the medium-induced force in a certain regime of temperatures and L.…”