%0 Book Section %1 statphys23_0380 %A Grueneberg, D. %A Diehl, H.W. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K casimir critical effect field finite-size phenomena point renormalization scaling statphys23 theory topic-2 %T Improved field theory results for thermodynamic Casimir forces in slabs with periodic boundary conditions %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=380 %X Thermodynamic Casimir forces in $ınfty^d-1L$ slabs with periodic boundary conditions are studied within the framework of the $n$-component $\phi^4$ model. Recent work 1 has revealed that conventional renormalization-group (RG) improved perturbation theory in $d=4-\epsilon$ dimensions breaks down at the bulk critical temperature $T_c,ınfty$ whenever Landau theory involves a zero mode (as it does in the case of periodic boundary conditions). The reorganization of field theory introduced there is utilized to compute finite-size scaling functions of the Casimir force and the excess free energy. The results show that the approach cures a number of salient features by which previous results based on conventional RG improved perturbation theory were plagued, such as qualitatively incorrect dependence on $n$, problematic behavior for $L/\xi_ınfty0$ (where $\xi_ınfty$ is the bulk correlation length), and violation of analyticity requirements of the scaling functions at $T_c,ınfty$. \noindent\newline 1) H.~W. Diehl, Daniel Grueneberg and M.~A. Shpot, Europhys. Lett. 75, 241 (2006)

@incollection{statphys23_0380, abstract = {Thermodynamic Casimir forces in $\infty^{d-1}\times L$ slabs with periodic boundary conditions are studied within the framework of the $n$-component $\phi^4$ model. Recent work [1] has revealed that conventional renormalization-group (RG) improved perturbation theory in $d=4-\epsilon$ dimensions breaks down at the bulk critical temperature $T_{\mathrm{c},\infty}$ whenever Landau theory involves a zero mode (as it does in the case of periodic boundary conditions). The reorganization of field theory introduced there is utilized to compute finite-size scaling functions of the Casimir force and the excess free energy. The results show that the approach cures a number of salient features by which previous results based on conventional RG improved perturbation theory were plagued, such as qualitatively incorrect dependence on $n$, problematic behavior for $L/\xi_\infty\to 0$ (where $\xi_\infty$ is the bulk correlation length), and violation of analyticity requirements of the scaling functions at $T_{\mathrm{c},\infty}$. \noindent\newline{} 1) H.~W. Diehl, Daniel Grueneberg and M.~A. Shpot, Europhys. Lett. \textbf{75}, 241 (2006)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Grueneberg, D. and Diehl, H.W.}, biburl = {https://www.bibsonomy.org/bibtex/2efd652a151f09d302081ca07d41bbed8/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {73c2eb6b58642a5d7e2ab884b53a223f}, intrahash = {efd652a151f09d302081ca07d41bbed8}, keywords = {casimir critical effect field finite-size phenomena point renormalization scaling statphys23 theory topic-2}, month = {9-13 July}, timestamp = {2007-06-20T10:16:18.000+0200}, title = {Improved field theory results for thermodynamic Casimir forces in slabs with periodic boundary conditions}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=380}, year = 2007 }