Phenomenology of local scale invariance: From conformal invariance to dynamical scaling
May, 2002Citations per year
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
References(99)
Figures(13)