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Relevance of space anisotropy in the critical behavior of m-axial Lifshitz points | | H. W. Diehl
; M. A. Shpot
; R. K. P. Zia
; | | Date: |
15 Jul 2003 | | Journal: | Phys.Rev. B68 (2003) 224415 DOI: 10.1103/PhysRevB.68.224415 | | Subject: | Statistical Mechanics | cond-mat.stat-mech hep-th | | Abstract: | The critical behavior of $d$-dimensional systems with $n$-component order parameter $m{phi}$ 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 $m{phi}$ 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, $sum_{alpha=1}^m(partial_alpha^2m{phi})^2$, 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 ${mathbb R}^m$. | | Source: | arXiv, cond-mat/0307355 | | Services: | Forum | Review | PDF | Favorites | |
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