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3d Ising Spin-Glasses in a Magnetic Field and Mean-Field Theory

We present the results of extensive computer simulations of 3d Ising spin-glasses in the presence of a uniform magnetic field. We compute the internal energy, the magnetization, the spin-spin overlap probability distribution P(q), the link-link overlap probability distribution Pe(qe) and the spin-glass susceptibility χSG for different volumes and temperatures. All of our results are compatible with mean-field behaviour. We find that P(q) and Pe(qe) are nontrivial and non-self-averaging and χSG shows an increase with the linear size L of the system as χSG ∼ Lω. Our estimate is ω = 1.80 ± 0.25 at T = 0.83. We also find evidence in favour of ultrametricity. In another set of simulations we study the copy overlap Q(ε) as a function of the coupling between copies ε. Q(ε) becomes steeper around ε ∼ 0 as L increases, in agreement with the previous set of simulations.