Scaling and Persistence in the Two-Dimensional Ising Model

Details Scaling and Persistence in the Two-Dimensional Ising Model Scaling and Persistence in the Two-Dimensional Ising Model

2000-04-10

arxiv.org/abs/cond-mat/0004148v1

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/0305-4470/33/47/305

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 $d_f\sim 1.58$.

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