Voter Dynamics on an Ising Ladder: Coarsening and Persistence

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.

arXiv commentreplaced with published version (text somewhat expanded): 11 pages, 2 figures

References in corpus (14)

• Theory of Phase Ordering Kinetics
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• Dynamics of Majority Rule
• Does a Single Zealot Affect an Infinite Group of Voters ?
• Incomplete ordering of the voter model on small-world networks
• Exact first-passage exponents of 1D domain growth: relation to a reaction diffusion model
• Exact Results for Kinetics of Catalytic Reactions
• Conservation laws for the voter model in complex networks
• Bifurcations and Patterns in Compromise Processes
• Coarsening and persistence in the voter model
• Freezing and Slow Evolution in a Constrained Opinion Dynamics Model
• Large deviations and nontrivial exponents in coarsening systems
• Persistence in the Voter model: continuum reaction-diffusion approach
• Persistence in One-dimensional Ising Models with Parallel Dynamics

Cited by in corpus (5)

• A new model of binary opinion dynamics: coarsening and effect of disorder
• Local Persistence in the Directed Percolation Universality Class
• Opinion dynamics model with domain size dependent dynamics: novel features and new universality class
• Noise driven dynamic phase transition in a a one dimensional Ising-like model
• Novel ballistic to diffusive crossover in the dynamics of a one dimensional Ising model with variable range of interaction