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The very existence of a phase transition for spin glasses in an externalmagnetic field is controversial, even in high dimensions. We carry out massivesimulations of the Ising spin-glass in a field, in six dimensions (which,according to classical, but not generally accepted, field-theoretical studies,is the upper critical dimension). We find a phase transition and compute thecritical exponents, that are found to be compatible with their mean-fieldvalues. We also find that the replica-symmetric Hamiltonian describes thescaling of the renormalized couplings near the phase transition.

Second order phase transition in the six-dimensional Ising spin glass on a field