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Power laws in physics

Nature Reviews Physics volume 4, pages 501–503 (2022)Cite this article

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Getting the most from power-law-type data can be challenging. James Sethna points out some of the pitfalls in studying power laws arising from emergent scale invariance, as well as important opportunities.

Power laws arise in many fields of knowledge — from word usage in linguistics, to income distributions in economics. There is an enormous literature observing and calculating power laws in nature. Publication of new, interesting results may involve data spanning one to two decades1: we need good tools to show that the power laws are real and accurate. In short, power laws are easy to fit, but challenging to measure and interpret well2. What are the particular challenges in studying power laws stemming from emergent scale invariance, a focus of much of statistical physics? And what opportunities exist to extract more science from the data?

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Fig. 1: Power laws and avalanche sizes in a random-field Ising model under an increasing field.

References

  1. Avnir, D., Biham, O., Lidar, D. & Malcai, O. Is the geometry of nature fractal? Science 279, 39–40 (1998).

    Article  ADS  Google Scholar 

  2. Newman, M. Power laws, pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351 (2005).

    Article  ADS  Google Scholar 

  3. Sethna, J. P., Dahmen, K. A. & Myers, C. R. Crackling noise. Nature 410, 242–250 (2001).

    Article  ADS  Google Scholar 

  4. Liarte, D. B. et al. Universal scaling for disordered viscoelastic matter I: Dynamic susceptibility at the onset of rigidity. Preprint at https://arxiv.org/abs/2103.07474 (2021).

  5. Adam, S., Brouwer, P. W., Sethna, J. P. & Waintal, X. Enhanced mesoscopic fluctuations in the crossover between random-matrix ensembles. Phys. Rev. B 66, 165310 (2002).

    Article  ADS  Google Scholar 

  6. Chen, Y., Papanikolaou, S., Sethna, J. P., Zapperi, S. & Durin, G. Avalanche spatial structure and multivariable scaling functions; sizes, heights, widths, and views through windows. Phys. Rev. E 84, 061103 (2011).

    Article  ADS  Google Scholar 

  7. Chen, Y.-J., Zapperi, S. & Sethna, J. P. Crossover behavior in interface depinning. Phys. Rev. E 92, 022146 (2015).

    Article  ADS  Google Scholar 

  8. Hayden, L. X., Raju, A. & Sethna, J. P. Unusual scaling for two-dimensional avalanches: Curing the faceting and scaling in the lower critical dimension. Phys. Rev. Res. 1, 033060 (2019).

    Article  Google Scholar 

  9. Perkovic, O., Dahmen, K. & Sethna, J. P. Avalanches, Barkhausen noise, and plain old criticality. Phys. Rev. Lett. 75, 4528–4531 (1995).

    Article  ADS  Google Scholar 

  10. Sethna, J. P. Crackling crossover. Nat. Phys. 3, 518–519 (2007).

    Article  Google Scholar 

Download references

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  1. LASSP, Physics Department, Cornell University, Ithaca, NY, USA

    James P. Sethna

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  1. James P. Sethna
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Correspondence to James P. Sethna.

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Sethna, J.P. Power laws in physics. Nat Rev Phys 4, 501–503 (2022). https://doi.org/10.1038/s42254-022-00491-x

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