Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

Details Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

2004-04-20

arxiv.org/abs/cond-mat/0404477v2

J. Stat. Mech. (2006) P02004

Physics

Condensed Matter

Disordered Systems and Neural Networks

9 pages, 6 figures

Scientific paper

We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a way that closely resembles the relaxation in a large number of complex systems in nature. Such apparent scale invariance simply results in the model from summing over many exponential relaxations, each with a scale which is determined by the curvature of the domain wall at which the avalanche originates. The claim that scale invariance in a nonequilibrium setting is to be associated with criticality is therefore not supported. Some hints that may help in checking this experimentally are discussed.

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