Thermodynamic Casimir effects involving interacting field theories with zero modes
| dc.creator | Grüneberg, Daniel | |
| dc.creator | Diehl, H. W. | |
| dc.date | 2007-10-24 | |
| dc.date | 2008-03-14 | |
| dc.date.accessioned | 2026-07-07T09:26:30Z | |
| dc.date.available | 2026-07-07T09:26:30Z | |
| dc.description | Systems 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.description | 23 pages, 10 figures | |
| dc.identifier | https://arxiv.org/abs/0710.4436 | |
| dc.identifier | http://arxiv.org/abs/0710.4436 | |
| dc.identifier | Phys. Rev. B 77, 115409 (2008) | |
| dc.identifier | doi:10.1103/PhysRevB.77.115409 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/156773 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Thermodynamic Casimir effects involving interacting field theories with zero modes | |
| dc.type | text |