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)
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