Voter Dynamics on an Ising Ladder: Coarsening and Persistence

TL;DR

This paper investigates the coarsening and persistence behavior of Ising spins on a ladder under voter dynamics, revealing algebraic decay of domain walls and specific persistence exponents, and compares these with other models.

Contribution

It provides a detailed analysis of voter dynamics on a ladder, including numerical values of persistence exponents and their relation to other models, which was not previously established.

Findings

Domain wall density decreases as t^{-1/2}

Persistence probability decays as t^{-θ} with θ ≈ 0.44 (sequential) and 0.88 (parallel)

Results are compared with 1D, 2D voter models and zero-temperature Glauber dynamics

Abstract

Coarsening and persistence of Ising spins on a ladder is examined under voter dynamics. The density of domain walls decreases algebraically with time as $t^-{1/2}$ for sequential as well as parallel dynamics. The persistence probability decreases as $t^{-\theta_{s}}$ under sequential dynamics, and as $t^{-\theta_{p}}$ under parallel dynamics where $\theta_{p} = 2 \theta_{s} \approx .88$. Numerical values of the exponents are explained. The results are compared with the voter model on one and two dimensional lattices, as well as Ising model on a ladder under zero-temperature Glauber dynamics.