Relevance of space anisotropy in the critical behavior of m-axial Lifshitz points

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dc.creatorDiehl, H. W.
dc.creatorShpot, M. A.
dc.creatorZia, R. K. P.
dc.date2003-07-15
dc.date2003-10-27
dc.date.accessioned2026-07-07T02:52:22Z
dc.date.available2026-07-07T02:52:22Z
dc.descriptionThe critical behavior of $d$-dimensional systems with $n$-component order parameter $\bmϕ$ is studied at an $m$-axial Lifshitz point where a wave-vector instability occurs in an $m$-dimensional subspace ${\mathbb R}^m$ ($m{>}1$). Field theoretic renormalization group techniques are exploited to examine the effects of terms in the Hamiltonian that break the rotational symmetry of the Euclidean group ${\mathbb E}(m)$. The framework for considering general operators of second order in $\bmϕ$ and fourth order in the derivatives $\partial_α$ with respect to the Cartesian coordinates $x_α$ of ${\mathbb R}^m$ is presented. For the specific case of systems with cubic anisotropy, the effects of having an additional term, $\sum_{α=1}^m(\partial_α^2\bmϕ)^2$, are investigated in an $ε$ expansion about the upper critical dimension $d^{*}(m)=4+m/2$. Its associated crossover exponent is computed to order $ε^2$ and found to be positive, so that it is a \emph{relevant} perturbation on a model isotropic in ${\mathbb R}^m$.
dc.descriptionRevtex4, 11 pages, to appear in PRB; v2: some additional references and minor changes
dc.identifierhttps://arxiv.org/abs/cond-mat/0307355
dc.identifierhttp://arxiv.org/abs/cond-mat/0307355
dc.identifierPhys.Rev. B68 (2003) 224415
dc.identifierdoi:10.1103/PhysRevB.68.224415
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/21815
dc.subjectStatistical Mechanics
dc.subjectHigh Energy Physics - Theory
dc.titleRelevance of space anisotropy in the critical behavior of m-axial Lifshitz points
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