The European Physical Journal Special Topics

, Volume 226, Issue 4, pp 605–625

From dynamical scaling to local scale-invariance: a tutorial

Review

DOI: 10.1140/epjst/e2016-60336-5

Cite this article as:
Henkel, M. Eur. Phys. J. Spec. Top. (2017) 226: 605. doi:10.1140/epjst/e2016-60336-5
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Part of the following topical collections:
  1. Recent Advances in Phase Transitions and Critical Phenomena

Abstract

Dynamical scaling arises naturally in various many-body systems far from equilibrium. After a short historical overview, the elements of possible extensions of dynamical scaling to a local scale-invariance will be introduced. Schrödinger-invariance, the most simple example of local scale-invariance, will be introduced as a dynamical symmetry in the Edwards-Wilkinson universality class of interface growth. The Lie algebra construction, its representations and the Bargman superselection rules will be combined with non-equilibrium Janssen-de Dominicis field-theory to produce explicit predictions for responses and correlators, which can be compared to the results of explicit model studies. At the next level, the study of non-stationary states requires to go over, from Schrödinger-invariance, to ageing-invariance. The ageing algebra admits new representations, which acts as dynamical symmetries on more general equations, and imply that each non-equilibrium scaling operator is characterised by two distinct, independent scaling dimensions. Tests of ageing-invariance are described, in the Glauber-Ising and spherical models of a phase-ordering ferromagnet and the Arcetri model of interface growth.

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© EDP Sciences and Springer 2017

Authors and Affiliations

  1. 1.Rechnergestützte Physik der Werkstoffe, Institut für Baustoffe (IfB), ETH ZürichZürichSwitzerland

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