Boundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis

Simple item page
dc.creatorDiehl, H. W.
dc.creatorShpot, M. A.
dc.creatorPrudnikov, P. V.
dc.date2005-12-28
dc.date.accessioned2026-07-07T06:53:43Z
dc.date.available2026-07-07T06:53:43Z
dc.descriptionSemi-infinite $d$-dimensional systems with an $m$-axial bulk Lifshitz point are considered whose ($d-1$)-dimensional surface hyper-plane is oriented perpendicular to one of the $m$ modulation axes. An $n$-component $ϕ^4$ field theory describing the bulk and boundary critical behaviour when (i) the Hamiltonian can be taken to have O(n) symmetry and (ii) spatial anisotropies breaking its Euclidean symmetry in the $m$-dimensional coordinate subspace of potential modulation directions may be ignored is investigated. The long-distance behaviour at the ordinary surface transition is mapped onto a field theory with the boundary conditions that both the order parameter $\bmϕ$ and its normal derivative $\partial_n\bmϕ$ vanish at the surface plane. The boundary-operator expansion is utilized to study the short-distance behaviour of $\bmϕ$ near the surface. Its leading contribution is found to be controlled by the boundary operator $\partial_n^2\bmϕ$. The field theory is renormalized for dimensions $d$ below the upper critical dimension $d^*(m)=4+m/2$, with a corresponding surface source term $\propto \partial_n^2\bmϕ$ added. The anomalous dimension of this boundary operator is computed to first order in $ε=d^*-d$. The result is used in conjunction with scaling laws to estimate the value of the single independent surface critical exponent $β_{\mathrm{L}1}^{(\mathrm{ord},\perp)}$ for $d=3$. Our estimate for the case $m=n=1$ of a uniaxial Lifshitz point in Ising systems is in reasonable agreement with published Monte Carlo results.
dc.descriptionsubmitted to J. Phys. A: Math and Gen, special issue on Renormalization Group 2005 as featured in the international workshop Renormalization Group 2005, Helsinki, Finland 30 August - 3 September 2005 (http://theory.physics.helsinki.fi/~rg2005/)
dc.identifierhttps://arxiv.org/abs/cond-mat/0512681
dc.identifierhttp://arxiv.org/abs/cond-mat/0512681
dc.identifierJ. Phys. A: Math. Gen. 39 (2006) 7927-7942
dc.identifierdoi:10.1088/0305-4470/39/25/S09
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105688
dc.subjectStatistical Mechanics
dc.subjectSoft Condensed Matter
dc.titleBoundary critical behaviour at m-axial Lifshitz points of semi-infinite systems with a surface plane perpendicular to a modulation axis
dc.typetext

Files

Collections

arXiv