Coarsening kinetics in one-dimensional spin systems with long-range interactions: from voter to Ising
Abstract
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, $$J(r) \propto r^{-\alpha }$$ 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 $$p = 1$$ p = 1 and $$p = 2$$ p = 2 , while for $$p \ge 3$$ p ≥ 3 it falls into the universality class of the Ising model. Graphical abstract
Fields of Study & Subjects
Opinion Dynamics and Social Influence
Theoretical and Computational Physics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- The European Physical Journal B
- Publisher
- Springer Science and Business Media LLC
- Volume
- 99
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN