Ordering kinetics with long-range interactions: interpolating between voter and Ising models
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866909318767443968 |
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| author | Corberi, Federico Russo, Salvatore dello Smaldone, Luca |
| author_facet | Corberi, Federico Russo, Salvatore dello Smaldone, Luca |
| contents | We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a lattice, each of which takes in an elementary move the state of the majority of $p$ other agents at distances $r$ chosen with probability $P(r)\propto r^{-α}$. For $p=2$ the model can be exactly mapped onto the case with $p=1$, which amounts to the voter model with long-range interactions decaying algebraically. For $3\le p<\infty$, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant $J(r)=P(r)$ quenched to small finite temperatures. In the limit $p\to \infty$, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for $ p > 3$ a closed set of differential equations cannot be found, we employed numerical simulations to address this case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_06917 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ordering kinetics with long-range interactions: interpolating between voter and Ising models Corberi, Federico Russo, Salvatore dello Smaldone, Luca Statistical Mechanics We study the ordering kinetics of a generalization of the voter model with long-range interactions, the $p$-voter model, in one dimension. It is defined in terms of boolean variables $S_{i}$, agents or spins, located on sites $i$ of a lattice, each of which takes in an elementary move the state of the majority of $p$ other agents at distances $r$ chosen with probability $P(r)\propto r^{-α}$. For $p=2$ the model can be exactly mapped onto the case with $p=1$, which amounts to the voter model with long-range interactions decaying algebraically. For $3\le p<\infty$, instead, the dynamics falls into the universality class of the one-dimensional Ising model with long-ranged coupling constant $J(r)=P(r)$ quenched to small finite temperatures. In the limit $p\to \infty$, a crossover to the (different) behavior of the long-range Ising model quenched to zero temperature is observed. Since for $ p > 3$ a closed set of differential equations cannot be found, we employed numerical simulations to address this case. |
| title | Ordering kinetics with long-range interactions: interpolating between voter and Ising models |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2404.06917 |