Time-Delay Induced Dimensional Crossover in the Voter Model

Mina Kim, Jae Dong Noh

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We investigate the ordering dynamics of the voter model with time-delayed interactions. The dynamical process in the d-dimensional lattice is shown to be equivalent to the first passage problem of a random walker in the (d1)-dimensional strip of a finite width determined by the delay time. The equivalence reveals that the time delay leads to the dimensional crossover from the (d1)-dimensional scaling behavior at a short time to the d-dimensional scaling behavior at a long time. The scaling property in both regimes and the crossover time scale are obtained analytically, which are confirmed with the numerical simulation results.

Original languageEnglish
Article number168302
JournalPhysical Review Letters
Issue number16
StatePublished - 17 Apr 2017


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