Four-dimensional spin glasses in a magnetic field have a mean-field-like phase

By using numerical simulations we show that the four-dimensional J = ±1 Edwards Anderson spin glass in magnetic field undergoes a mean-field-like phase transition. We use a dynamical approach: we simulate large lattices (of volume V) and work out the behaviour of the system in a limit where both t and V go to infinity, but where the limit V → ∞ is taken first. By showing that the dynamic overlap q converges to a value smaller than the static one we exhibit replica symmetry breaking. The critical exponents are compatible with those obtained by mean-field computations.