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arXiv · 1410.4007

Persistence in the two dimensional ferromagnetic Ising model

Thibault Blanchard·Leticia F. Cugliandolo·Marco Picco
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Abstract

We present very accurate numerical estimates of the time and size dependence of the zero-temperature local persistence in the $2d$ ferromagnetic Ising model. We show that the effective exponent decays algebraically to an asymptotic value $\theta$ that depends upon the initial condition. More precisely, we find that $\theta$ takes one universal value $0.199(2)$ for initial conditions with short-range spatial correlations as in a paramagnetic state, and the value $0.033(1)$ for initial conditions with the long-range spatial correlations of the critical Ising state. We checked universality by working with a square and a triangular lattice, and by imposing free and periodic boundary conditions. We found that the effective exponent suffers from stronger finite size effects in the former case.

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Thibault Blanchard, Leticia F. Cugliandolo, Marco Picco. 2014-10-15. Persistence in the two dimensional ferromagnetic Ising model. https://doi.org/10.1088/1742-5468%2F2014%2F12%2Fp12021

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