Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions
| dc.creator | Diehl, H. W. | |
| dc.creator | Chamati, H. | |
| dc.date | 2008-10-29 | |
| dc.date | 2009-03-16 | |
| dc.date.accessioned | 2026-07-07T12:53:02Z | |
| dc.date.available | 2026-07-07T12:53:02Z | |
| dc.description | The critical dynamics of relaxational stochastic models with nonconserved $n$-component order parameter $\bmϕ$ and no coupling to other slow variables ("model A") is investigated in film geometries for the cases of periodic and free boundary conditions. The Hamiltonian $\mathcal{H}$ governing the stationary equilibrium distribution is taken to be O(n) symmetric and to involve, in the case of free boundary conditions, the boundary terms $\int_{\mathfrak{B}_j}\mathring{c}_j ϕ^2/2$ associated with the two confining surface planes $\mathfrak{B}_j$, $j=1,2$, at $z=0$ and $z=L$, where the enhancement variables $\mathring{c}_j$ are presumed to be subcritical or critical. A field-theoretic RG study of the dynamic critical behavior at $d=4-ε$ bulk dimensions is presented, with special attention paid to the cases where the classical theories involve zero modes at $T_{c,\infty}$. This applies when either both $\mathring{c}_j$ take the critical value $\mathring{c}_{\text{sp}}$ associated with the special surface transition, or else periodic boundary conditions are imposed. Owing to the zero modes, the $ε$ expansion becomes ill-defined at $T_{c,\infty}$. Analogously to the static case, the field theory can be reorganized to obtain a well-defined small-$ε$ expansion involving half-integer powers of $ε$, modulated by powers of $\lnε$. Explicit results for the scaling functions of $T$-dependent finite-size susceptibilities at temperatures $T\ge T_{c,\infty}$ and of layer and surface susceptibilities at the bulk critical point are given to orders $ε$ and $ε^{3/2}$, respectively. For the case of periodic boundary conditions, the consistency of the expansions to $O(ε^{3/2})$ with exact large-$n$ results is shown. | |
| dc.description | Latex file with 8 eps files included; text added in conclusions and abstract, typos corrected | |
| dc.identifier | https://arxiv.org/abs/0810.5244 | |
| dc.identifier | http://arxiv.org/abs/0810.5244 | |
| dc.identifier | Phys. Rev. B 79, 104301 (2009) | |
| dc.identifier | doi:10.1103/PhysRevB.79.104301 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223487 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Dynamic critical behavior of model A in films: Zero-mode boundary conditions and expansion near four dimensions | |
| dc.type | text |