Persistence in the two dimensional ferromagnetic Ising model

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 θ that depends upon the initial condition. More precisely, we find that θ 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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Submitted on : Wednesday, March 4, 2015 - 3:23:59 PM
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T Blanchard, L. F. Cugliandolo, M Picco. Persistence in the two dimensional ferromagnetic Ising model. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2014, 2014 (12), pp.P12021. ⟨10.1088/1742-5468/2014/12/P12021⟩. ⟨hal-01122795⟩

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