1996/10/31 by Malte Henkel · 125 citations
Mathematics · Physics and Astronomy · #Anisotropy #Black Holes and Theoretical Physics #Condensed matter physics #Conformal map #Conformal symmetry #Function (biology) #Generalization #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Scale invariance #Scaling #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #Theoretical and Computational Physics #Thermodynamics #cond-mat.stat-mech #hep-lat #hep-th
paper · pdf · doi:10.1103/physrevlett.78.1940
published in Physical Review Letters 78(10), 1940-1943 (American Physical Society) · 4 pages Revtex, no figures, with file multicol.sty, to appear in PRL
arxiv created 1997/02/23 · openalex publication_date 1997/03/10 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A new set of infinitesimal transformations generalizing scale invariance for strongly anisotropic critical systems is considered. It is shown that such a generalization is possible if the anisotropy exponent \ensuremathθ\phantom\rule0ex0ex=\phantom\rule0ex0ex2/N, with N\phantom\rule0ex0ex=\phantom\rule0ex0ex1,2,3…. Differential equations for the two-point function are derived and explicitly solved for all values of N. Known special cases are conformal invariance ( N\phantom\rule0ex0ex=\phantom\rule0ex0ex2) and Schr"odinger invariance ( N\phantom\rule0ex0ex=\phantom\rule0ex0ex1). For N\phantom\rule0ex0ex=\phantom\rule0ex0ex4 and N\phantom\rule0ex0ex=\phantom\rule0ex0ex6, the results contain as special cases the exactly known scaling forms obtained for the spin-spin correlation function in the axial next-nearest-neighbor spherical model at its Lifshitz points of first and second order.