Improved field theory results for thermodynamic Casimir forces in slabs with periodic boundary conditions
D. Grueneberg, and H. Diehl. Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Abstract
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)
%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
}