Low-temperature scaling for systems with random fields and anisotropies

Random fields (or anisotropies) shift the lower critical dimensionality of spin systems from dc0 to dc. For dimensionalities dc0<d<dc at low temperatures T, the magnetization has a discontinuity (from zero to M) when (the average square field) approaches zero. The correlation length diverges as. The structure factor is shown to scale as S(q,)=dS»(q). Simple assumptions on scaling near T=0 yield "=1(dc-d), with dc=4 for continuous symmetry spins and dc=2 for Ising spins.