THEORY OF THE CRITICAL-STATE OF LOW-DIMENSIONAL SPIN-GLASS

We analyse the critical region of finite-(d)-dimensional Ising spin gl ass, in particular the limit of d closely above the lower critical dim ension de. At criticality the thermally active degrees of freedom are surfaces (of width zero) enclosing clusters of spins that may reverse with respect to their environment. The surfaces are organised in finit e interacting structures. These may be called protodroplets, since in the off-critical limit they reduce to the Fisher and Huse droplets. Th is picture provides an explanation for the phenomenon of critical chao s discovered earlier. It also implies that the spin-spin and energy-en ergy correlation functions are multifractal and we present scaling law s that describe them. Several of our results should be verifiable in M onte Carlo studies at finite temperature in d = 3.