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

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