Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

P. I. Hurtado; J. Marro; P. L. Garrido

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Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

P. I. Hurtado·J. Marro·P. L. Garrido

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Abstract

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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P. I. Hurtado, J. Marro, P. L. Garrido. 2006-02-09. Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena. https://arxiv.org/abs/cond-mat/0404477

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