2007/10/31 by Daniel Grüneberg, H. W. Diehl · 3 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Mechanical and Optical Resonators #Quantum Electrodynamics and Casimir Effect #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevb.77.115409
published as Phys. Rev. B 77, 115409 (2008) · 23 pages, 10 figures
openalex publication_date 2008/03/06 · arxiv created 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Systems with an O(n) symmetrical Hamiltonian are considered in a d-dimensional slab geometry of macroscopic lateral extension and finite thickness L that undergo a continuous bulk phase transition in the limit L\ensuremath→\ensuremath∞. The effective forces induced by thermal fluctuations at and above the bulk critical temperature T_c,\ensuremath∞ (thermodynamic Casimir effect) are investigated below the upper critical dimension d*=4 by means of field-theoretic renormalization-group methods for the case of periodic and special-special boundary conditions, where the latter correspond to the critical enhancement of the surface interactions on both boundary planes. As shown previously [Europhys. Lett. 75, 241 (2006)], the zero modes that are present in Landau theory at T_c,\ensuremath∞ make conventional renormalization-group-improved perturbation theory in 4\ensuremath-ϵ dimensions ill-defined. The revised expansion introduced there is utilized to compute the scaling functions of the excess free energy and the Casimir force for temperatures T\ensuremath\geqslantT_c,\ensuremath∞ as functions of L\ensuremath≡L∕\ensuremathξ_\ensuremath∞, where \ensuremathξ_\ensuremath∞ is the bulk correlation length. Scaling functions of the L-dependent residual free energy per area are obtained, whose L\ensuremath→0 limits are in conformity with previous results for the Casimir amplitudes \ensuremathΔC to O(ϵ3∕2) and display a more reasonable small-L behavior inasmuch as they approach the critical value \ensuremathΔC monotonically as L\ensuremath→0. Extrapolations to d=3 for the Ising case n=1 with periodic boundary conditions are in fair agreement with Monte Carlo results. In the case of special-special boundary conditions, extrapolations to d=3 are hampered by the fact that the one-loop result for the inverse finite-size susceptibility becomes negative for some values of L when ϵ\ensuremath\gtrsim0.83.