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

Abstract

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 P_e(q_e) and the spin-glass susceptibility χ_SG for different volumes and temperatures. All of our results are compatible with mean-field behaviour. We find that P(q) and P_e(q_e) are nontrivial and non-self-averaging and χ_SG shows an increase with the linear size L of the system as χ_SG ~ L^ω. 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.