Scaling and Persistence in the Two-Dimensional Ising Model

Abstract

The spatial distribution of persistent spins at zero-temperature in the pure two-dimensional Ising model is investigated numerically. A persistence correlation length, $\xi (t)\sim t^Z$ is identified such that for length scales $r<<\xi (t)$ the persistent spins form a fractal with dimension $d_f$; for length scales $r>>\xi (t)$ the distribution of persistent spins is homogeneous. The zero-temperature persistence exponent, $\theta$, is found to satisfy the scaling relation $\theta =Z(2-d_f)$ with $\theta =0.209\pm 0.002,Z=1/2$ and $d_f\sim 1.58$.

13 pages, TeX; 4 postscript figures. Submitted to J Phys A

References in corpus (3)

• Persistence in Nonequilibrium Systems
• Persistence with Partial Survival
• Zero Temperature Dynamics of the Weakly Disordered Ising Model

Cited by in corpus (15)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Kinetics of Coalescence, Annihilation, and the q-State Potts Model in One Dimension
• Zero-Temperature Coarsening in the Two-Dimensional Long-Range Ising Model
• Persistence in the two dimensional ferromagnetic Ising model
• Phase-ordering kinetics in the Allen-Cahn (Model A) class: universal aspects elucidated by electrically-induced transition in liquid crystals
• Fractality in Persistence Decay and Domain Growth during Ferromagnetic Ordering: Dependence upon initial correlation
• Fraction of uninfected walkers in the one-dimensional Potts model
• Persistence in Cluster--Cluster Aggregation
• Uninfected random walkers in one dimension
• Persistence in q-state Potts model: A Mean-Field approach
• Minority spin dynamics in non-homogeneous Ising model: diverging timescales and exponents
• Persistence Exponents and Scaling In Two Dimensional XY model and A Nematic Model
• Local and global persistence exponents of two quenched continuous lattice spin models
• Approach to zigzag and checkerboard patterns in spatially extended systems
• Aging Exponents for Nonequilibrium Dynamics following Quenches from Critical Point