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Universal scaling in real dimension

Author

Listed:
  • Giacomo Bighin

    (Universität Heidelberg)

  • Tilman Enss

    (Universität Heidelberg)

  • Nicolò Defenu

    (ETH Zürich)

Abstract

The concept of universality has shaped our understanding of many-body physics, but is mostly limited to homogenous systems. Here, we present a study of universality on a non-homogeneous graph, the long-range diluted graph (LRDG). Its scaling theory is controlled by a single parameter, the spectral dimension ds, which plays the role of the relevant parameter on complex geometries. The graph under consideration allows us to tune the value of the spectral dimension continuously also to noninteger values and to find the universal exponents as continuous functions of the dimension. By means of extensive numerical simulations, we probe the scaling exponents of a simple instance of $$O({{{{{{{\mathcal{N}}}}}}}})$$ O ( N ) symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.

Suggested Citation

  • Giacomo Bighin & Tilman Enss & Nicolò Defenu, 2024. "Universal scaling in real dimension," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-48537-1
    DOI: 10.1038/s41467-024-48537-1
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    References listed on IDEAS

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