These tools will no longer be maintained as of December 31, 2024. Archived website can be found here. PubMed4Hh GitHub repository can be found here. Contact NLM Customer Service if you have questions.
Pubmed for Handhelds
PUBMED FOR HANDHELDS
Search MEDLINE/PubMed
Title: Large-n approach to thermodynamic Casimir effects in slabs with free surfaces. Author: Diehl HW, Grüneberg D, Hasenbusch M, Hucht A, Rutkevich SB, Schmidt FM. Journal: Phys Rev E Stat Nonlin Soft Matter Phys; 2014 Jun; 89(6):062123. PubMed ID: 25019741. Abstract: The classical n-vector ϕ{4} model with O(n) symmetrical Hamiltonian H is considered in a ∞{2}×L slab geometry bounded by a pair of parallel free surface planes at separation L. Standard quadratic boundary terms implying Robin boundary conditions are included in H. The temperature-dependent scaling functions of the excess free energy and the thermodynamic Casimir force are computed in the large-n limit for temperatures T at, above, and below the bulk critical temperature T_{c}. Their n=∞ limits can be expressed exactly in terms of the spectrum and eigenfunctions of a self-consistent one-dimensional Schrödinger equation. This equation is solved by numerical means for two distinct discretized versions of the model: in the first ("model A"), only the coordinate z across the slab is discretized and the integrations over momenta conjugate to the lateral coordinates are regularized dimensionally; in the second ("model B"), a simple cubic lattice with periodic boundary conditions along the lateral directions is used. Renormalization-group ideas are invoked to show that, in addition to corrections to scaling ∝L{-1}, anomalous ones ∝L{-1}lnL should occur. They can be considerably decreased by taking an appropriate g→∞ (T_{c}→∞) limit of the ϕ{4} interaction constant g. Depending on the model A or B, they can be absorbed completely or to a large extent in an effective thickness L_{eff}=L+δL. Excellent data collapses and consistent high-precision results for both models are obtained. The approach to the low-temperature Goldstone values of the scaling functions is shown to involve logarithmic anomalies. The scaling functions exhibit all qualitative features seen in experiments on the thinning of wetting layers of {4}He and Monte Carlo simulations of XY models, including a pronounced minimum of the Casimir force below T_{c}. The results are in conformity with various analytically known exact properties of the scaling functions.[Abstract] [Full Text] [Related] [New Search]