NDLI: Fluctuation-induced forces in periodic slabs: Breakdown of expansion at the bulk critical point and revised field theory

Content Provider	EDP Sciences
Author	H. W. Diehl Daniel Grüneberg M. A. Shpot
Abstract	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-ϵ 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 ϵ, the small-ϵ 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 .
Ending Page	247
Starting Page	241
Page Count	7
File Format	HTM / HTML PDF
ISSN	02955075
Alternate Webpage(s)	https://epljournal.edpsciences.org/articles/epl/abs/2006/14/epl9434/epl9434.html
e-ISSN	12864854
Issue Number	2
Journal	Europhysics Letters
Volume Number	75
DOI	10.1209/epl/i2006-10090-0
Language	English
Publisher	EDP Sciences
Publisher Date	2006-07-01
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	© EDP Sciences, 2006
Subject Keyword	Critical point phenomena Liquid thin films Field theory
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy

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