Field-theoretical formulation of the spin-glass transition in the Potts model with short-ranged random-exchange interaction

The spin-glass (SG) transition in the q-state Potts model with short-ranged random-exchange interaction is formulated by means of field theory. The critical properties are discussed using a 6-ε expansion method carried out to one-loop order. When q(integer) is greater than 3, the transition is found to be of first order. Some implications within the one-loop calculation for the case $q=3$ are discussed. Comparisons are made with the recent work of Nishimori and Stephen, Elderfield and Sherrington, and Erzan and Lage on the infinite-range model.