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  • Letter
  • Open Access

XY model for cascade transfer

Tomohiro Tanogami and Shin-ichi Sasa

  • Department of Physics, Kyoto University, Kyoto 606-8502, Japan

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Phys. Rev. Research 4, L022015 – Published 22 April, 2022

DOI: https://doi.org/10.1103/PhysRevResearch.4.L022015

Abstract

We propose a modified XY model in which cascade transfer emerges from spatially local interactions where the spin corresponds to the “velocity” of a turbulent field. For this model, we theoretically calculate the scale-to-scale energy flux and the equal time correlation function in d dimensions. The result indicates an inverse energy cascade with the non-Kolmogorov energy spectrum proportional to k−3. We also numerically confirm the result for the cases of d=2 and d=3. We thus conclude that the cascade transfer in our model represents a different universality class from standard fluid turbulence.

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Phys. Rev. Research 4, L022015– Published 22 April, 2022
  • Received 25 June 2021
  • Accepted 24 March 2022
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