Low temperature behaviour of 3-D spin glasses in a magnetic field

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Abstract
We present the results of two sets of numerical simulations of 3-d Ising spin-glasses in the presence of an uniform magnetic field. In the first set, among other quantities, we compute the spin-spin overlap probability distribution P (q ), the link-link overlap probability distribution P e(qe) and the spin-glass susceptibility χ SG for different volumes and temperatures. The results are in good agreement with mean-field behaviour : P(q) and P e(qe) are non trivial and non self-averaging and χSG shows an increase with the linear size L of the system as χSG ∼ Lω. Our estimate is ω = 1,8 ± 0.25 at T = 0.83. In the second set of simulations a small coupling ε is introduced between two copies of the system and the copy overlap Q(ε) is computed as a function of ε. Q(ε) becomes steeper around ε ∼ 0 as L increases, in agreement with the previous set of simulations. Our data seem anyhow incompatible with the alternatives to mean-field theory proposed so far