2001/06/30 by M. A. Shpot, M. Shpot, H. W. Diehl
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1016/s0550-3213(01)00309-1
published as Nucl. Phys. B 612 (2001) 340-372 · 42 pages, 1 figure; to appear in Nuclear Physics B; footnote added, minor changes in v2
arxiv created 2001/07/10 · openalex publication_date 2001/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the critical behavior that d-dimensional systems with short-range forces and a n-component order parameter exhibit at Lifshitz points whose wave-vector instability occurs in a m-dimensional isotropic subspace of \mathbb Rd. Utilizing dimensional regularization and minimal subtraction of poles in d=4+m\over 2-ε dimensions, we carry out a two-loop renormalization-group (RG) analysis of the field-theory models representing the corresponding universality classes. This gives the beta function βu(u) to third order, and the required renormalization factors as well as the associated RG exponent functions to second order, in u. The coefficients of these series are reduced to m-dependent expressions involving single integrals, which for general (not necessarily integer) values of m∈ (0,8) can be computed numerically, and for special values of m analytically. The ε expansions of the critical exponents ηl2, ηl4, νl2, νl4, the wave-vector exponent βq, and the correction-to-scaling exponent are obtained to order ε2. These are used to estimate their values for d=3. The obtained series expansions are shown to encompass both isotropic limits m=0 and m=d.