Universal scaling in real dimension

Year: 2024

Authors: Bighin G., Enss T., Defenu N.

Autors Affiliation: Heidelberg Univ, Inst Theoret Phys, D-69120 Heidelberg, Germany; Swiss Fed Inst Technol, Inst Theoret Phys, Wolfgang Pauli Str 27, CH-8093 Zurich, Switzerland.

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(N) symmetric models on the LRDG showing quantitative agreement with the theoretical prediction of universal scaling in real dimensions.

Journal/Review: NATURE COMMUNICATIONS

Volume: 15 (1)      Pages from: 4207-1  to: 4207-9

More Information: We gladly acknowledge Giacomo Gori for his help in determining the spectral dimension from the numerical data. N.D. acknowledges stimulating discussions with Mehran Kardar. This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC2181/1-390900948 (the Heidelberg STRUCTURES Excellence Cluster) and by the Swiss National Science Foundation (SNSF) under project funding ID: 200021 207537. The authors acknowledge support from the state of Baden-Wuerttemberg through bwHPC. This research was supported in part by grant NSF PHY-1748958 to the Kavli Institute for Theoretical Physics (KITP).
KeyWords: Mermin-wagner Theorem; Monte-carlo Method; Critical Exponents; Phase-transitions; Symmetry-breaking; Spherical Model; Field-theories; Random-walks; O(n) Models; Behavior
DOI: 10.1038/s41467-024-48537-1

Citations: 1
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