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• W1971428062 abstract "Systems described by n-component ϕ4 models in a ∞d − 1×L slab geometry of finite thickness L are considered at and above their bulk critical temperatureTc,∞. The renormalization-group improved perturbation theory commonly employed to investigate the fluctuation-induced forces (thermodynamic Casimir effect) in d = 4 − 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 Tc,∞. The leading contributions to the critical Casimir amplitudes Δper and Δsp,spbeyond two-loop order are ∼ (u*)(3 − )/2, whereu* = O() is the value of the renormalized ϕ4 coupling at the infrared-stable fixed point. Besides integer powers of , the small- expansions of these amplitudes involve fractional powers k/2, with k ⩾ 3, and powers of ln . Explicit results to order 3/2 are presented for Δper and Δsp,sp, which are used to estimate their values at d = 3." @default.
• W1971428062 created "2016-06-24" @default.
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• W1971428062 date "2006-07-01" @default.
• W1971428062 modified "2023-09-25" @default.
• W1971428062 title "Fluctuation-induced forces in periodic slabs: Breakdown of epsilon expansion at the bulk critical point and revised field theory" @default.
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• W1971428062 doi "https://doi.org/10.1209/epl/i2006-10090-0" @default.
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