Phenomenology of local scale invariance: From conformal invariance to dynamical scaling

May, 2002
73 pages
Published in:
  • Nucl.Phys.B 641 (2002) 405-486
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Abstract: (Elsevier)
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent θ or a dynamical exponent z . For a given value of θ (or z ), we construct local scale transformations, which can be viewed as scale transformations with a space–time-dependent dilatation factor. Two distinct types of local scale transformations are found. The first type may describe strongly anisotropic scaling of static systems with a given value of θ , whereas the second type may describe dynamical scaling with a dynamical exponent z . Local scale transformations act as a dynamical symmetry group of certain non-local free-field theories. Known special cases of local scale invariance are conformal invariance for θ =1 and Schrödinger invariance for θ =2.
Note:
  • Latex, 73 pages, with 9 figures. Minor corrections, final form
  • statistical mechanics
  • critical phenomena
  • operator: algebra
  • scaling
  • boundary condition
  • numerical calculations: Monte Carlo
  • bibliography