We study a general model for non-Gaussian $1/f$ noise based on an infinite range quantum Ising spin system in the paramagnetic state, or, equivalently, interacting two-level classical fluctuators. We identify a dilatation interaction term in the dynamics which survives the thermodynamic limit and circumvents the central limit theorem to produce non-Gaussian noise even when the equilibrium distribution is that of noninteracting spins. The resulting second spectrum (“noise of the noise”) itself has a universal $1/f$ form which we analyze within a dynamical mean-field approximation.

• Received 14 June 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.127205