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Universal scaling in real dimension
Giacomo Bighin1, Tilman Enss1, Nicolò Defenu2
1Institut für Theoretische Physik, Universität Heidelberg, 69120, Heidelberg, Germany.
Nature Communications
|May 17, 2024
Summary
We studied universality in physics on a complex, non-homogeneous graph, the long-range diluted graph (LRDG). Our findings reveal universal scaling behavior controlled by the spectral dimension, extending universality to new complex systems.
Area of Science:
- Complex systems physics
- Statistical mechanics
- Graph theory
Background:
- Universality is a key concept in many-body physics, typically studied in homogeneous systems.
- Understanding universality in non-homogeneous or complex systems remains a significant challenge.
- The spectral dimension (ds) is a critical parameter for describing scaling in complex geometries.
Purpose of the Study:
- To investigate universality on a non-homogeneous graph, the long-range diluted graph (LRDG).
- To explore how the spectral dimension (ds) controls scaling theory in complex geometries.
- To determine universal scaling exponents as continuous functions of the spectral dimension.
Main Methods:
- Theoretical analysis of scaling theory on the LRDG.
- Continuous tuning of the spectral dimension (ds) to non-integer values.
- Extensive numerical simulations of symmetric models on the LRDG.
Main Results:
- The spectral dimension (ds) was identified as the single controlling parameter for scaling theory on the LRDG.
- Universal scaling exponents were found to be continuous functions of the spectral dimension.
- Numerical simulations showed quantitative agreement with theoretical predictions for universal scaling.
Conclusions:
- Universality can be extended to non-homogeneous systems like the LRDG.
- The spectral dimension is a crucial parameter for understanding universal scaling on complex graphs.
- This work provides a framework for studying universality in diverse complex systems.
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