Fluctuation-induced forces in periodic slabs: Breakdown of expansion at the bulk critical point and revised field theoryH. W. Diehl1, Daniel Grüneberg1 and M. A. Shpot1, 2
1 Fachbereich Physik, Universität Duisburg-Essen - Campus Essen D-45117 Essen, Germany
2 Institute for Condensed Matter Physics - 79011 Lviv, Ukraine
received 2 May 2006; accepted in final form 23 May 2006
published online 14 June 2006
Systems described by n-component models in a slab geometry of finite thickness L are considered at and above their bulk critical temperature . The renormalization-group improved perturbation theory commonly employed to investigate the fluctuation-induced forces ("thermodynamic Casimir effect") in bulk dimensions is re-examined. It is found to be ill-defined beyond two-loop order because of infrared singularities when the boundary conditions are such that the free propagator in slab geometry involves a zero-energy mode at bulk criticality. This applies to periodic boundary conditions and the special-special ones corresponding to the critical enhancement of the surface interactions on both confining plates. The field theory is reorganized such that a small- expansion results which remains well behaved down to . The leading contributions to the critical Casimir amplitudes and beyond two-loop order are , where is the value of the renormalized coupling at the infrared-stable fixed point. Besides integer powers of , the small- expansions of these amplitudes involve fractional powers , with , and powers of . Explicit results to order are presented for and , which are used to estimate their values at d=3.
05.70.Jk - Critical point phenomena.
68.15.+e - Liquid thin films.
11.10.-z - Field theory.
© EDP Sciences 2006