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Numerical study of the transition of the four dimensional Random Field Ising Model

Roberto Sacconi
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Abstract

We study numerically the region above the critical temperature of the four dimensional Random Field Ising Model. Using a cluster dynamic we measure the connected and disconnected magnetic susceptibility and the connected and disconnected overlap susceptibility. We use a bimodal distribution of the field with $ h_R=0.35T $ for all temperatures and a lattice size L=16. Through a least-square fit we determine the critical exponents $ γ$ and $ \barγ $. We find the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above $ T_c $. Accordingly with other simulations we find $ \barγ=2γ$. In this case we have a scaling theory with two indipendet critical exponents

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Roberto Sacconi. 1997-09-05. Numerical study of the transition of the four dimensional Random Field Ising Model. https://doi.org/10.1088/0305-4470%2F31%2F16%2F005

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