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arXiv:cond-mat/9708058 · Journal of Physics A Mathematical and General

Numerical study of the transition of the four-dimensional random field Ising model

Roberto Sacconi

Published Apr 24, 1998• 0 citations
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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 for all temperatures and a lattice size L = 16. Through a least-square fit we determine the critical temperature at which the two susceptibilities diverge. We also determine the critical exponents and . We find that the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above . Accordingly with other simulations we find . In this case we have a scaling theory with two independent critical exponents.

DOI
10.1088/0305-4470/31/16/005

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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 for all temperatures and a lattice size L = 16. Through a least-square fit we determine the critical temperature at which the two susceptibilities diverge. We also determine the critical exponents and . We find that the magnetic susceptibility and the overlap susceptibility diverge at two different temperatures. This is coherent with the existence of a glassy phase above . Accordingly with other simulations we find . In this case we have a scaling theory with two independent critical exponents.
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The phase transition of the three-dimensional random field Ising model with a discrete (+or-h) field distribution is investigated by extensive Monte Carlo simulations. Values of the critical exponents for the correlation length, specific heat, susceptibility, disconnected susceptibility and magnetization are determined simultaneously via finite size scaling. While the magnetization appears to be discontinuous, the specific heat appears to saturate, indicating no latent heat. Sample-to-sample fluctuations of the susceptibility are consistent with the droplet picture for the transition.
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