Local scale invariance and its applications to strongly anisotropic critical phenomena

Details Local scale invariance and its applications to strongly anisotropic critical phenomena Local scale invariance and its applications to strongly anisotropic critical phenomena

2003-07-25

arxiv.org/abs/cond-mat/0307649v1

Physics

Condensed Matter

Statistical Mechanics

Latex2e 23 pages, with 4 figures included. Review to appear in `Progress in Mathematical Physics', Nova Science (New York 2003

Scientific paper

The generalization of dynamical scaling to local scale invariance is reviewed. Starting from a recapitulation of the phenomenology of ageing phenomena, the generalization of dynamical scaling to local scale transformation for any given dynamical exponent $z$ is described and the two distinct types of local scale invariance are presented. The special case $z=2$ and the associated Ward identity of Schr\"odinger invariance is treated. Local scale invariance predicts the form of the two-point functions. Existing confirmations of these predictions for (I) the Lifshitz points in spin systems with competing interactions such as the ANNNI model and (II) non-equilibrium ageing phenomena as occur in the kinetic Ising model with Glauber dynamics are described.

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