Non-universal critical Casimir force in confined ${}^4$He 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 $\sim |\mathbf{x}{|}^{-d-\sigma }$ 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 $L\gtrsim \xi$ (correlation length) we find that the van der Waals interaction causes a leading non-universal non-scaling contribution of $O({\xi }^2{L}^{-d-\sigma })$ to the critical temperature dependence of the Casimir force above $T_{\lambda }$ that dominates the universal scaling contribution $\sim e^{-L/\xi }$ predicted by earlier theories. For the specific heat we find subleading non-scaling contributions of $O(L^{-1})$ and $O(L^{-d-\sigma })$.

2 pages, submitted to LT23 Proceedings on June 14, 2002, accepted for publication in Physica B on September 12, 2002

References in corpus (3)

• Subleading long-range interactions and violations of finite size scaling
• Two-point correlation function in systems with van der Waals type interaction
• Non-universal size dependence of the free energy of confined systems near criticality

Cited by in corpus (5)

• Nonuniversal finite-size scaling in anisotropic systems
• Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
• Diversity of critical behavior within a universality class
• Critical Casimir force in slab geometry with finite aspect ratio: analytic calculation above and below $T_c$
• Scaling and nonscaling finite-size effects in the Gaussian and the mean spherical model with free boundary conditions