# Ordering kinetics with long-range interactions: interpolating between voter and Ising models Source: [Ordering kinetics with long-range interactions: interpolating between voter and Ising models]() Collection index: [llms.txt]() Data updated: 2025-10-25T06:36:35.629Z Authors: Federico Corberi, Salvatore dello Russo, Luca Smaldone Published: 2024-04-10T11:09:04.000Z ## Abstract 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 $P(r)\\propto r^{-\\alpha}$. 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()