Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes
| dc.creator | Diehl, H. W. | |
| dc.creator | Gerwinski, A. | |
| dc.creator | Rutkevich, S. | |
| dc.date | 2003-08-25 | |
| dc.date | 2003-10-27 | |
| dc.date.accessioned | 2026-07-07T02:53:05Z | |
| dc.date.available | 2026-07-07T02:53:05Z | |
| dc.description | The critical behavior of semi-infinite $d$-dimensional systems with $n$-component order parameter $\bmϕ$ and short-range interactions is investigated at an $m$-axial bulk Lifshitz point whose wave-vector instability is isotropic in an $m$-dimensional subspace of $\mathbb{R}^d$. The associated $m$ modulation axes are presumed to be parallel to the surface, where $0\le m\le d-1$. An appropriate semi-infinite $|\bmϕ|^4$ model representing the corresponding universality classes of surface critical behavior is introduced. It is shown that the usual O(n) symmetric boundary term $\propto \bmϕ^2$ of the Hamiltonian must be supplemented by one of the form $\mathringλ \sum_{α=1}^m(\partial\bmϕ/\partial x_α)^2$ involving a dimensionless (renormalized) coupling constant $λ$. The implied boundary conditions are given, and the general form of the field-theoretic renormalization of the model below the upper critical dimension $d^*(m)=4+{m}/{2}$ is clarified. Fixed points describing the ordinary, special, and extraordinary transitions are identified and shown to be located at a nontrivial value $λ^*$ if $ε\equiv d^*(m)-d>0$. The surface critical exponents of the ordinary transition are determined to second order in $ε$. Extrapolations of these $ε$ expansions yield values of these exponents for $d=3$ in good agreement with recent Monte Carlo results for the case of a uniaxial ($m=1$) Lifshitz point. The scaling dimension of the surface energy density is shown to be given exactly by $d+m (θ-1)$, where $θ=ν_{l4}/ν_{l2}$ is the anisotropy exponent. | |
| dc.description | revtex4, 31 pages with eps-files for figures, uses texdraw to generate some graphs; to appear in PRB; v2: some references and additional remarks added, labeling in figure 1 and some typos corrected | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0308483 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0308483 | |
| dc.identifier | Phys. Rev. B 68, 224428 (2003) (30 pages) | |
| dc.identifier | doi:10.1103/PhysRevB.68.224428 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/22074 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Soft Condensed Matter | |
| dc.title | Boundary critical behavior at m-axial Lifshitz points for a boundary plane parallel to the modulation axes | |
| dc.type | text |