Dresden 2009 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 1: Statistical physics I (general)

DY 1.3: Talk

Monday, March 23, 2009, 11:00–11:15, HÜL 386

Critical Casimir Forces in Strongly Anisotropic Systems — •Matthias Burgsmüller and Hans Werner Diehl — Fachbereich Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany

Strongly anisotropic systems are considered in a d-dimensional film geometry. Such systems involve two (or more) distinct correlation lengths ξ_β and ξ_α that scale as nontrivial powers of each other: i.e. ξ_α∼ξ_β^θ with θ≠ 1. Thus two fundamental orientations, ⊥ and ||, for which the surface normal is oriented along an α or β direction must be distinguished. The confinement of critical fluctuations caused by the film’s boundary planes is shown to induce effective forces F_C that decay as F_C≈ −(∂/∂ L)Δ_⊥,|| L^−ζ_⊥,|| as a function of film thickness L, where the decay exponents ζ_⊥,|| and Casimir amplitudes Δ_⊥,|| differ for ⊥ and || orientation. To corroborate these findings, n-vector models with an m-axial bulk Lifshitz point are investigated by means of RG methods below the upper critical dimension d^*(m)=4+m/2 under various boundary conditions. The exponents ζ_⊥,|| are determined, and explicit results to one or zeroth loop order are presented for several Casimir amplitudes Δ_⊥,||.