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• W2024643249 abstract "The critical behavior of $d$-dimensional systems with $n$-component order parameter $bm{phi}$ 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 $bm{phi}$ and fourth order in the derivatives $partial_alpha $ with respect to the Cartesian coordinates $x_alpha $ of ${mathbb R}^m$ is presented. For the specific case of systems with cubic anisotropy, the effects of having an additional term, $sum_{alpha=1}^m(partial_alpha^2bm{phi})^2$, are investigated in an $epsilon$ expansion about the upper critical dimension $d^{*}(m)=4+m/2$. Its associated crossover exponent is computed to order $epsilon^2$ and found to be positive, so that it is a emph{relevant} perturbation on a model isotropic in ${mathbb R}^m$." @default.
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• W2024643249 date "2003-12-17" @default.
• W2024643249 modified "2023-09-23" @default.
• W2024643249 title "Relevance of space anisotropy in the critical behavior ofm-axial Lifshitz points" @default.
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• W2024643249 doi "https://doi.org/10.1103/physrevb.68.224415" @default.
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