Luca Smaldone — Università degli studi di Salerno #
Ordering kinetics with long-range interactions: interpolating between voter and Ising models #
We study the ordering kinetics of a one-dimensional generalization of the voter model with long-range, power-law interactions, the $p$-voter model. In this model, the agent, or spin, located at a site of a lattice adopts the majority state among $p$ other agents, whose distances $r$ are drawn from a probability distribution $P(r) \propto r^{-\alpha}$.
For $p=2$, the model can be mapped onto the voter model with the same long-range interactions. For $3 \leq p < \infty$, the dynamics belongs to the universality class of the one-dimensional Ising model with long-range coupling $J(r)=P(r)$, quenched to small but finite temperatures. In the limit $p \to \infty$, we observe a crossover to the distinct behavior of the long-range Ising model quenched to zero temperature.