Spin-glass field theory in the condensed phase continued to below d=6

Field theory has been held back from being able to describe the spin-glass condensed phase in physical dimensions by the strong infrared divergences of its (bare) propagators with small overlaps, e.g. the zero overlap replicon propagator G 00 R (p) approximately p -4 . Here the authors examine the effect of fluctuations at the one-loop level on the equation of state for the Parisi order parameter q(x). They find that above d=6, the one-loop term does not change the analytical behaviour of q(x) approximately x. Below d=6, the loop contribution becomes dominant and radically changes the classical behaviour into q(x) approximately x rho , rho =3/(d-3) approximately 1+ in /3. Besides, since the infrared divergences are driven by the small-x behaviour, they also get G 00 R (p) approximately p -4+2 in 3/. This remark is also valid away from T c since the weakening of infrared singularities by fluctuations occurs solely via the (stronger) vanishing of q(x) near zero overlaps. Consistently taking account of fluctuations should thus allow a fully detailed field theory description of the condensed phase below d=6.