https://doi.org/10.1140/epjb/s10051-026-01122-5
Topical Review - Statistical and Nonlinear Physics
Coarsening kinetics in one-dimensional spin systems with long-range interactions: from voter to Ising
1
Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, Italy
2
INFN Sezione di Napoli, Gruppo collegato di Salerno, Napoli, Italy
3
Dipartimento di Matematica e Fisica, Università della Campania, Viale Lioncoln, 5, 81100, Caserta, Italy
4
Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano, 10, 50019, Sesto Fiorentino, Italy
5
INFN Sezione di Firenze, via G. Sansone, 1, 50019, Sesto Fiorentino, Italy
a
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Received:
25
October
2025
Accepted:
6
January
2026
Published online:
9
February
2026
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, 
. 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 
and 
, while for 
it falls into the universality class of the Ising model.
© The Author(s) 2026
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