  The spin-glass transition in a field in finite dimension is analyzed directly
at zero temperature using a perturbative loop expansion around the Bethe
lattice solution. The loop expansion is generated by the $M$-layer construction
whose first diagrams are evaluated numerically and analytically. The Ginzburg
criterion, from both the paramagnetic and spin-glass phase, reveals that the
upper critical dimension below which mean-field theory fails is $D_\text{U}=8$,
at variance with the classic results $D_\text{U}=6$ yielded by
finite-temperature replica field theory. The different outcome follows from two
crucial properties: finite-connectivity of the lattice and zero temperature.
They both also lead to specific features of the replica-symmetry-breaking
phase.
