The noisy voter model

The noisy voter model is a spin system on a graph which may be obtained from the basic voter model by adding spontaneous flipping from 0 to 1 and from 1 to 0 at each site. Using duality, we obtain exact formulas for some important time-dependent and equilibrium functionals of this process. By letting the spontaneous flip rates tend to zero, we get the basic voter model, and we calculate the exact critical exponents associated with this “phase transition”. Finally, we use the noisy voter model to present an alternate view of a result due to Cox and Griffeath on clustering in the two-dimensional basic voter model.