Coarsening kinetics in spin systems with long-range interactions: from voter to Ising
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911433259745280 |
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| author | Corberi, Federico Lippiello, Eugenio Politi, Paolo Smaldone, Luca |
| author_facet | Corberi, Federico Lippiello, Eugenio Politi, Paolo Smaldone, Luca |
| contents | 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, $J(r) \propto r^{-α}$. 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 $p \ge 3$ it falls into the universality class of the Ising model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15410 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarsening kinetics in spin systems with long-range interactions: from voter to Ising Corberi, Federico Lippiello, Eugenio Politi, Paolo Smaldone, Luca Statistical Mechanics 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, $J(r) \propto r^{-α}$. 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 $p \ge 3$ it falls into the universality class of the Ising model. |
| title | Coarsening kinetics in spin systems with long-range interactions: from voter to Ising |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2510.15410 |