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Ground-state behavior of the 3d +/-J random-bond Ising model

Alexander K. Hartmann
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Abstract

Large numbers of ground states of the three-dimensional $\pm J$ random-bond Ising model are calculated for sizes up to $14^3$ using a combination of a genetic algorithm and Cluster-Exact Approximation. Several quantities are calculated as function of the concentration $p$ of the antiferromagnetic bonds. The critical concentration where the ferromagnetic order disappears is determined using the Binder cumulant of the magnetization. A value of $p_c=0.222\pm 0.005$ is obtained. From the finite-size behavior of the Binder cumulant and the magnetization critical exponents $ν=1.1 \pm 0.3$ and $β=0.2 \pm 0.1$ are calculated.

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Alexander K. Hartmann. 1998-08-18. Ground-state behavior of the 3d +/-J random-bond Ising model. https://doi.org/10.1103/physrevb.59.3617

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