  The de Almeida-Thouless (AT) line is the phase boundary in the
temperature--magnetic field plane of an Ising spin glass at which a continuous
(i.e. second-order) transition from a paramagnet to a replica-symmetry-breaking
(RSB) phase occurs, according to mean-field theory. Here, using field-theoretic
perturbative renormalization group methods on the Bray-Roberts reduced
Landau-Ginzburg-type theory for a short-range Ising spin glass in space of
dimension $d$, we show that at nonzero magnetic field the nature of the
corresponding transition is modified as follows: a) for $d-6$ small and
positive, with increasing field on the AT line first, the ordered phase just
below the transition becomes the so-called one-step RSB, instead of the full
RSB that occurs in mean-field theory; the transition on the AT line remains
continuous with a diverging correlation length. Then at a higher field, a
tricritical point separates the latter transition from a quasi-first-order one,
that is one at which the correlation length does not diverge, and there is a
jump in part of the order parameter, but no latent heat. The location of the
tricritical point tends to zero as $d\to6^+$; b) for $d\leq 6$, we argue that
the quasi-first-order transition could persist down to arbitrarily small
nonzero fields, with a transition to full RSB still expected at lower
temperature. Whenever the quasi-first-order transition occurs, it is at a
higher temperature than the AT transition would be for the same field,
preempting it as the temperature is lowered. We also draw attention to the
similarity of the "dynamically-frozen" state, which occurs at temperatures just
above the quasi-first-order transition, and the "metastate-average state" of
the one-step RSB phase, and discuss the issue of the number of pure states in
either.
