The phase transition of the four dimensional Ising spin glass in presence of a magnetic field is well described by a replica-symmetric field theory

Which is the field-theory for the spin-glass phase transition in a magnetic field? This is an open question in less than six dimensions. So far, perturbative computations have not found a stable fixed-point for the renormalization group flow. We tackle this problem through a numerical analysis of the Ising spin glass in four spatial dimensions (data obtained from the Janus collaboration) and in the Bethe lattice. We find strong numerical evidence supporting that the phase transition of the four dimensional Ising spin glass in a field is described by a replica-symmetric Hamiltonian.