Coarsening kinetics in one-dimensional spin systems with long-range interactions: from voter to Ising

Abstract: In this paper, we start reviewing the main features of the one-dimensional Ising model with long-range interactions, where the spin-spin coupling decays as a power law, J(r)∝r-α. We then discuss the key properties of the one-dimensional voter model, in which two agents (spins) at distance r interact with a power-law probability with the same form of J(r). The two models are compared, and the so-called p-voter model is presented, which provides a framework to interpolate between them. Specifically, the p-voter model reduces to the voter model for p=1 and p=2, while for p≥3 it falls into the universality class of the Ising model.