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arXiv · 2510.15410

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

Federico Corberi·Eugenio Lippiello·Paolo Politi·Luca Smaldone
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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, $J(r) \propto r^{-\alpha}$. 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 $p \ge 3$ it falls into the universality class of the Ising model.

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Federico Corberi, Eugenio Lippiello, Paolo Politi, Luca Smaldone. 2025-10-17. Coarsening kinetics in spin systems with long-range interactions: from voter to Ising. https://doi.org/10.1140/epjb%2Fs10051-026-01122-5

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