Ordering kinetics of the two-dimensional voter model with long-range interactions

We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance r with probability P(r)∝r^{-α}. The model is characterized by different regimes, as α is varied. For α>4, the...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. E 2024-03, Vol.109 (3-1), p.034133-034133, Article 034133
Main Authors: Corberi, Federico, Smaldone, Luca
Format: Article
Language:English
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance r with probability P(r)∝r^{-α}. The model is characterized by different regimes, as α is varied. For α>4, the behavior is similar to that of the nearest-neighbor model, with the formation of ordered domains of a typical size growing as L(t)∝sqrt[t], until consensus is reached in a time of the order of NlnN, with N being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as ρ(t)∝1/lnt. Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbor interactions. For 0
ISSN:2470-0045
2470-0053
DOI:10.1103/PhysRevE.109.034133