SHORT-RANGE POTTS SPIN-GLASS MODEL - RENORMALIZATION-GROUP METHOD

We study the phase diagram of the short-range Potts spin glass within the Migdal-Kadanoff renormalization group of the hypercubic lattices. Using some analytical approaches and performing the real-space renorma lization group of the problem we show that the model, for q>2, freezes into a Potts spin-glass phase at finite temperature, T(SG)not equal 0 , in d=4. This indicates an algebraic power-law decay of the correlati on functions in this low-temperature phase. We show that the Potts spi n-glass phase does not occur in d=3 for q>2 and calculate the lower cr itical dimension for all continuous values of q. The specific-heat cri tical exponent is found to be large and negative.