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We use the generic replica symmetric cubic field-theory to study thetransition of short range Ising spin glasses in a magnetic field around theupper critical dimension, d=6. A novel fixed-point is found, in addition to thewell-known zero magnetic field fixed-point, from the application of therenormalization group. In the spin glass limit, n going to 0, this fixed-pointgoverns the critical behaviour of a class of systems characterised by a singlecubic interaction parameter. For this universality class, the spin glasssusceptibility diverges at criticality, whereas the longitudinal mode remainsmassive. The third mode, the so-called anomalous one, however, behavesunusually, having a jump at criticality. The physical consequences of thisunusual behaviour are discussed, and a comparison with the conventional deAlmeida-Thouless scenario presented.Comment: 5 pages written in revtex4. Accepted for publication in Phys. Rev.  Let

Replica Field Theory and Renormalization Group for the Ising Spin Glass in an External Magnetic Field