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arXiv:cond-mat/0612418

Crackling Noise and Avalanches: Scaling, Critical Phenomena, and the Renormalization Group

James P. Sethna

Published Dec 15, 2006• 5 citations
arXivHTMLPDF

Abstract

In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the renormalization group, power laws, and universal scaling functions. These methods and tools were originally developed to understand continuous phase transitions in thermal and disordered systems, and we also introduce these more traditional applications as illustrations of the basic ideas and phenomena.

DOI
10.48550/arxiv.cond-mat/0612418

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In the past two decades or so, we have learned how to understand crackling noise in a wide variety of systems. We review here the basic ideas and methods we use to understand crackling noise - critical phenomena, universality, the renormalization group, power laws, and universal scaling functions. These methods and tools were originally developed to understand continuous phase transitions in thermal and disordered systems, and we also introduce these more traditional applications as illustrations of the basic ideas and phenomena.
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An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example---the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of 4He^{4}\mathrm{He}4He.
Abstract This chapter analyzes systems with emergent scale invariance -- fractal, self-similar behavior -- by developing the renormalization group. The renormalization group is an amazing abstraction. It describes the flow of the laws governing the system as one coarse-grains -- blurring out the short-distance or short-time details. In the huge space of possible systems (experimental and theoretical), a fixed point of the renormalization group will be the same after blurring and shrinking -- implying emergent scale invariance, a fractal self-similarity. The points which flow into the fixed point share its properties under rescaling -- implying universality, with behavior shared by theory and a wide variety of different experimental systems. The renormalization group also predicts universal power laws and universal functions, describing all behavior on long length and/or time scales. Exercises explore applications to the Ising model, the onset of lasing, superconductors, the onset of chaos, percolation, crackling noise and avalanches, earthquakes, random walks and diffusion, chemical reaction rate theory, and extreme value statistics.
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