Universality in long-range interacting systems: The effective dimension approach
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2024-10
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Journal Article
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Abstract
Dimensional correspondences have a long history in critical phenomena. Here, we review the effective dimension approach, which relates the scaling exponents of a critical system in d spatial dimensions with power-law decaying interactions rd+σ to a local system, i.e., with finite-range interactions, in an effective fractal dimension deff. This method simplifies the study of long-range models by leveraging known results from their local counterparts. While the validity of this approximation beyond the mean-field level has been long debated, we demonstrate that the effective dimension approach, while approximate for non-Gaussian fixed points, accurately estimates the critical exponents of long-range models with an accuracy typically larger than 97%. To do so, we review perturbative renormalization-group (RG) results, extend the approximation's validity using functional RG techniques, and compare our findings with precise numerical data from conformal bootstrap for the two-dimensional Ising model with long-range interactions.
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110 (4)
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44121
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American Physical Society
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09824 - Defenu, Nicolò / Defenu, Nicolò
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207537 - Out-of-equilibrium criticality of long-range interacting quantum systems (SNF)