XY model for cascade transfer

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.