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Symmetry 2015, 7(4), 2108-2133; doi:10.3390/sym7042108

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Groupe de Physique Statistique, Institut Jean Lamour (CNRS UMR 7198), Université de Lorraine Nancy, B.P. 70239, F-54506 Vandoeuvre-lès-Nancy Cedex, France
Academic Editor: Roman M. Cherniha
Received: 10 July 2015 / Revised: 28 October 2015 / Accepted: 29 October 2015 / Published: 13 November 2015
(This article belongs to the Special Issue Lie Theory and Its Applications)
View Full-Text   |   Download PDF [365 KB, uploaded 13 November 2015]   |  

Abstract

Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant n-point functions. These are important for the physical identification of n-point functions as responses or correlators. View Full-Text
Keywords: Schrödinger algebra; conformal Galilei algebra; ageing algebra; representations; causality; parabolic sub-algebra; holography; physical ageing Schrödinger algebra; conformal Galilei algebra; ageing algebra; representations; causality; parabolic sub-algebra; holography; physical ageing
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Henkel, M. Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions. Symmetry 2015, 7, 2108-2133.

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