Phenomenology of local scale invariance: from conformal invariance to dynamical scaling
By Malte Henkel. 2002
183 citations recorded by the source corpus.
Abstract 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 Schrodinger invariance for θ =2. The hypothesis of local scale invariance implies that two-point functions of quasiprimary operators satisfy certain linear fractional differential equations, which are constructed from commuting fractional derivatives. The explicit solution of these yields exact expressions for two-point correlators at equilibrium and for two-point response functions out of equilibrium. A particularly simple and general form is found for the two-time autoresponse function. These predictions are explicitly confirmed at the uniaxial Lifshitz points in the ANNNI and ANNNS models and in the aging behaviour of simple ferromagnets such as the kinetic Glauber–Ising model and the kinetic spherical model with a non-conserved order parameter undergoing either phase-ordering kinetics or non-equilibrium critical dynamics.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics
View Paper: https://www.semanticscholar.org/paper/a5d040698e86b8d4f682b276fc22065e5f0f4a6a
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
Citations in the corpus
- Conformal Carroll groups and BMS symmetry (2014, background): “3810; M. Henkel (2002) “Phenomenol- ogy of local scale invariance: from con- formal invariance to dynamical scaling,” Nucl.”
- The Schrödinger-Virasoro Lie Group and Algebra: Representation Theory and Cohomological Study (2006, background): “Unfortunately, it is finite-dimensional for every value of d, and its unitary irreducible representations are well-understood and classified (see [27]), giving very interesting though partial informations on twoand three-point functions in anisotropic and out-of-equilibrium statistical physics at cr”