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, $ξ(t)\sim t^Z$ is identified such that for length scales $r<<ξ(t)$ the persistent spins form a fractal with dimension $d_f$; for length scales $r>>ξ(t)$ the distribution of persistent spins is homogeneous. The zero-temperature persistence exponent, $θ$, is found to satisfy the scaling relation $θ= Z(2-d_f)$ with $θ=0.209\pm 0.002, Z=1/2$ and $d_f\sim 1.58$.

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