Short-range Potts spin-glass model: Renormalization-group method.

Abstract

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 renormalization group of the problem we show that the model, for q\ensuremath{\gtrsim}2, freezes into a Potts spin-glass phase at finite temperature, ${\mathit{T}}_{\mathrm{SG}}$\ensuremath{\ne}0, in d=4. This indicates an algebraic power-law decay of the correlation functions in this low-temperature phase. We show that the Potts spin-glass phase does not occur in d=3 for q\ensuremath{\gtrsim}2 and calculate the lower critical dimension for all continuous values of q. The specific-heat critical exponent is found to be large and negative. \textcopyright{} 1996 The American Physical Society.