2003/07/31 by H. W. Diehl, M. A. Shpot, R. K. P. Zia
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1103/physrevb.68.224415
published as Phys.Rev. B68 (2003) 224415 · Revtex4, 11 pages, to appear in PRB; v2: some additional references and minor changes
arxiv created 2003/10/27 · openalex publication_date 2003/12/17 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The critical behavior of d-dimensional systems with n-component order parameter \mathit\ensuremathφ is studied at an m-axial Lifshitz point where a wave-vector instability occurs in an m-dimensional subspace Rm (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 E(m). The framework for considering general operators of second order in \mathit\ensuremathφ and fourth order in the derivatives \ensuremath∂_\ensuremathα with respect to the Cartesian coordinates x_\ensuremathα of Rm is presented. For the specific case of systems with cubic anisotropy, the effects of having an additional term, \ensuremath∑_\ensuremathα=1m(\ensuremath∂_\ensuremathα2\mathit\ensuremathφ)2, are investigated in an \ensuremathε expansion about the upper critical dimension d*(m)=4+m/2. Its associated crossover exponent is computed to order \ensuremathε2 and found to be positive, so that it is a relevant perturbation on a model isotropic in Rm.