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We relate the anomalous noise found experimentally in spin ice to thesubdiffusion of magnetic monopoles. Because monopoles are emergent particles,they do not move in a structureless vacuum. Rather, the underlying spinensemble filters the thermal white noise, leading to non-trivial coevolution.Thus, monopoles can be considered as random walkers under the effect ofstochastic forces only as long as those are not trivially white, but insteadsubsume the evolution of the spin vacuum. Via this conceptualization, weconjecture relations between the color of the noise and other observables, suchas relaxation time, monopole density, the dynamic exponent, and the order ofthe annihilation reaction, which lead us to introduce spin ice specificcritical exponents in a neighborhood of the ice manifold.

The Colored Noise of Magnetic Monopoles: Subdiffusion in a Coevolving Vacuum and Spin Ice Exponents