Non-universal critical Casimir force in confined [formula omitted] 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 ).