On logarithmic extensions of local scale-invariance |
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Authors: | Malte Henkel |
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Affiliation: | Groupe de Physique Statistique, Département de Physique de la Matière et des Matériaux, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandœuvre lès Nancy Cedex, France |
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Abstract: | Ageing phenomena far from equilibrium naturally present dynamical scaling and in many situations this may be generalised to local scale-invariance. Generically, the absence of time-translation-invariance implies that each scaling operator is characterised by two independent scaling dimensions. Building on analogies with logarithmic conformal invariance and logarithmic Schrödinger-invariance, this work proposes a logarithmic extension of local scale-invariance, without time-translation-invariance. Carrying this out requires in general to replace both scaling dimensions of each scaling operator by Jordan cells. Co-variant two-point functions are derived for the most simple case of a two-dimensional logarithmic extension. Their form is compared to simulational data for autoresponse functions in several universality classes of non-equilibrium ageing phenomena. |
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Keywords: | Logarithmic conformal invariance Schrö dinger-invariance Dynamical scaling Local scale-invariance Directed percolation Kardar&ndash Parisi&ndash Zhang equation |
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