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Abstract
Exact ground states of three-dimensional
random field Ising magnets (RFIM) with Gaussian distribution of the
disorder are calculated
using graph-theoretical algorithms. Systems for different strengths $h$
of the random fields and sizes up to $N=96^3$ are considered.
By numerically differentiating the bond-energy with respect to $h$
a specific-heat like quantity is obtained, which does not appear to diverge at
the critical point but rather exhibits a cusp. We also consider the effect of
a
small
uniform magnetic field, which allows us to calculate the $T=0$
susceptibility. From a finite-size scaling analysis, we obtain the
critical exponents $\nu=1.32(7)$, $\alpha=-0.63(7)$, $\eta=0.50(3)$ and find
that the
critical strength of the random field is $h_c=2.28(1)$. We discuss the
significance of the result that $\alpha$ appears to be strongly negative.
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