Thermodynamic Casimir effects involving interacting field theories with zero modes

dc.creatorGrüneberg, Daniel
dc.creatorDiehl, H. W.
dc.date2007-10-24
dc.date2008-03-14
dc.date.accessioned2026-07-07T09:26:30Z
dc.date.available2026-07-07T09:26:30Z
dc.descriptionSystems 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 $L\to\infty$. The effective forces induced by thermal fluctuations at and above the bulk critical temperature $T_{c,\infty}$ (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 [\textit{Europhys. Lett.} \textbf{75}, 241 (2006)], the zero modes that are present in Landau theory at $T_{c,\infty}$ make conventional RG-improved perturbation theory in $4-ε$ 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 $T\geqT_{c,\infty}$ as functions of $\mathsf{L}\equiv L/ξ_\infty$, where $ξ_\infty$ is the bulk correlation length. Scaling functions of the $L$-dependent residual free energy per area are obtained whose $\mathsf{L}\to0$ limits are in conformity with previous results for the Casimir amplitudes $Δ_C$ to $O(ε^{3/2})$ and display a more reasonable small-$\mathsf{L}$ behavior inasmuch as they approach the critical value $Δ_C$ monotonically as $\mathsf{L}\to 0$.
dc.description23 pages, 10 figures
dc.identifierhttps://arxiv.org/abs/0710.4436
dc.identifierhttp://arxiv.org/abs/0710.4436
dc.identifierPhys. Rev. B 77, 115409 (2008)
dc.identifierdoi:10.1103/PhysRevB.77.115409
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/156773
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.titleThermodynamic Casimir effects involving interacting field theories with zero modes
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