2004/06/30 by H. W. Diehl, H W Diehl, S. Rutkevich +1 · 6 citations
Computer Science · Physics and Astronomy · #Critical exponent #Critical phenomena #Critical point (mathematics) #Exponent #Isotropy #Modulation (music) #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems #Renormalization group #Scaling #Surface (topology) #Theoretical and Computational Physics #Widom scaling #cond-mat.soft #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/0305-4470/37/36/001
published in Journal of Physics A Mathematical and General 37(36), 8575-8594 (Institute of Physics) · 21 pages, one figure included as eps file, uses IOP style files
openalex publication_date 2004/08/25 · arxiv created 2004/09/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The critical behaviour of d-dimensional semi-infinite systems with n-component order parameter \bmφ is studied at an m-axial bulk Lifshitz point whose wave-vector instability is isotropic in an m-dimensional subspace of ℝd. Field-theoretic renormalization group methods are utilised to examine the special surface transition in the case where the m potential modulation axes, with 0≤ m≤ d-1, are parallel to the surface. The resulting scaling laws for the surface critical indices are given. The surface critical exponent η_‖\rm sp, the surface crossover exponent Φ and related ones are determined to first order in ε=4+\casem2-d. Unlike the bulk critical exponents and the surface critical exponents of the ordinary transition, Φ is m-dependent already at first order in ε. The \Or(ε) term of η_‖\rm sp is found to vanish, which implies that the difference of β1\rm sp and the bulk exponent β is of order ε2.