2025/10/17 by Corberi, Federico, Lippiello, Eugenio, Politi, Paolo +1
#FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2510.15410
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.