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Fractal spin structures as origin of 1/f magnetic noise in superconducting circuits

We analyze recent data on the complex inductance of dc SQUIDs that show 1/f inductance noise highly correlated with conventional 1/f flux noise. We argue that these data imply a formation of long range order in fractal spin structures. We show that these structures appear naturally in a random system of spins with wide distribution of spin-spin interactions. We perform numerical simulations on the simplest model of this type and show that it exhibits $1/f^{1+ζ}$ magnetization noise with small exponent $ζ$ and reproduces the correlated behavior observed experimentally.