Replica symmetry breaking in and around six dimensions

Two, replica symmetry breaking specific, quantities of the Ising spin glass — the breakpoint x1x1 of the order parameter function and the Almeida–Thouless line — are calculated in six dimensions (the upper critical dimension of the replicated field theory used), and also below and above it. The results confirm that replica symmetry breaking does exist below d=6d=6, and also the tendency of its escalation for decreasing dimension continues. As a new feature, x1x1 has a nonzero and universal value for d<6d<6 at criticality. Near six dimensions we have x1c=3(6−d)+O[(6−d)2]x1c=3(6−d)+O[(6−d)2]. A method to expand a generic theory with replica equivalence around the replica symmetric one is also demonstrated.