CRITICAL-BEHAVIOR OF SHORT-RANGE POTTS GLASSES

We study by means of Monte Carlo simulations and the numerical transfer matrix technique the critical behavior of the short range p = 3 state Potts glass model in dimensions d = 2, 3, 4 with both Gaussian and bimodal (+/- J) nearest neighbor interactions on hypercubic lattices employing finite size scaling ideas. In d = 2 in addition the degeneracy of the glass ground state is computed as a function of the number of Potts states for p = 3, 4, 5 and compared to that of the antiferromagnetic ground state. Our data indicate a transition into a glass phase at T = 0 in d = 2 with an algebraic singularity, a T = 0 transition in d = 3 with an essential singularity of the form chi is similar to exp (const. T-2), and an algebraic singularity at T almost-equal-to 0.25 in d = 4. We conclude that the lower critical dimension of the present model is d(c) = 3 or very close to it. Some of the critical exponents are estimated and their respective values discussed.