Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Comment
  • Published:

Disentangling scaling arguments to empower complex systems analysis

Nature Physics volume 16, pages 1086–1088 (2020)Cite this article

Subjects

Matters Arising to this article was published on 02 November 2020

Scaling arguments provide valuable analysis tools across physics and complex systems yet are often employed as one generic method, without explicit reference to the various mathematical concepts underlying them. A careful understanding of these concepts empowers us to unlock their full potential.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Two distinct types of scaling analysis.

References

  1. Ising, E. Z. Phys. 31, 253–258 (1925).

    Article  ADS  Google Scholar 

  2. McCoy, B. M. & Wu, T. T. The Two-Dimensional Ising Model (Courier Corporation, 2014).

  3. Goldenfeld, N. Lectures on Phase Transitions and the Renormalization Group (CRC, 2018).

  4. Grimmett, G. R. Percolation (Springer, 1999).

  5. West, G. B. Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies (Penguin, 2017).

  6. D’Souza, R. M. & Nagler, J. Nat. Phys. 11, 531–538 (2015).

    Article  Google Scholar 

  7. Newman, M. E. J. Contemp. Phys. 46, 323–351 (2005).

    Article  ADS  Google Scholar 

  8. Clauset, A., Shalizi, C. R. & Newman, M. E. SIAM Rev. 51, 661–703 (2009).

    Article  ADS  MathSciNet  Google Scholar 

  9. Taylor, B. Methodus Incrementorum Directa & Inversa [Direct and Reverse Methods of Incrementation] Prop. VII, Thm 3, Cor. 2 (London, 1715). [Translated into English: Struik, D. J. A Source Book in Mathematics 1200–1800 329–332 (Harvard Univ. Press, 1969).]

  10. Altland, A. & von Delft, J. Mathematics for Physicists: Introductory Concepts and Methods (Cambridge Univ. Press, 2019).

  11. Bender, C. M. & Orszag, S. A. Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory (Springer, 2013).

  12. Miller, P. D. Applied Asymptotic Analysis (AMS, 2006).

  13. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Nat. Phys. 15, 403–412 (2019).

    Article  Google Scholar 

  14. Timme, M. & Nagler, J. Nat. Phys. 15, 308–309 (2019).

    Article  Google Scholar 

  15. Peng, J., Lin, W. & Kurths, J. Nat. Phys. https://doi.org/10.1038/s41567-020-1025-3 (2020).

  16. Hens, C., Harush, U., Haber, S., Cohen, R. & Barzel, B. Nat. Phys. https://doi.org/10.1038/s41567-020-1027-1 (2020).

Download references

Author information

Authors and Affiliations

  1. Institute for Theoretical Physics, Center for Advancing Electronics Dresden (cfaed), and Center of Excellence Physics of Life, Technical University of Dresden, Dresden, Germany

    Marc Timme & Malte Schröder

Authors
  1. Marc Timme
    View author publications

    Search author on:PubMed Google Scholar

  2. Malte Schröder
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Marc Timme.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Timme, M., Schröder, M. Disentangling scaling arguments to empower complex systems analysis. Nat. Phys. 16, 1086–1088 (2020). https://doi.org/10.1038/s41567-020-01063-5

Download citation

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41567-020-01063-5

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing