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Scaling and Persistence in the Two-Dimensional Ising Model

S. Jain·H. Flynn
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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 $d_f\sim 1.58$.

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S. Jain, H. Flynn. 2000-04-10. Scaling and Persistence in the Two-Dimensional Ising Model. https://doi.org/10.1088/0305-4470%2F33%2F47%2F305

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