FINITE-SIZE-SCALING IN THE P-STATE MEAN-FIELD POTTS GLASS - A MONTE-CARLO INVESTIGATION

The p-state mean-field Potts glass with bimodal bond distribution (+/- J) is studied by Monte Carlo simulations, both for p=3 and p = 6 slate s, for system sizes from N = 5 to N = 120 spins, considering particula rly the finite-size scaling behavior at the exactly known glass transi tion temperature T-c. It is shown that for p=3 the moments g((k)) of t he spin-glass order parameter satisfy a simple scaling behavior, g((k) ) proportional to N-k/3 (f) over tilde(k){N-1/3(1 - T/T-c)}, k=1, 2, 3 ,..., (f) over tilde(k) being the appropriate scaling function and T t he temperature. Also the specific heat maxima have a similar behavior, c(V)(max) proportional to const - N-1/3, while moments of the magneti zation scale as m((k)) proportional to N-k/2. The approach of the posi tions T,,, of these specific heat maxima to T-c as N --> infinity is n onmonotonic. For p=6 the results are compatible with a first-order tra nsition, q((k)) --> (q(jump))(k) as N---> infinity, but since the orde r parameter q(jump) at T-c is rather small, a behavior q((k)) proporti onal to N-k/3 as Ni co also is compatible with the data. Thus no firm conclusions on the finite-size behavior of the order parameter can be drawn. The specific heat maxima c(V)(max) behave qualitatively in the same way as for p=3, consistent with the prediction that there is no l atent heat. A speculative phenomenological discussion of finite-size s caling for such transitions is given. For small N (N less than or equa l to 15 for p = 3, N less than or equal to 12 for p = 6) the Monte Car lo data are compared to exact partition function calculations, and exc ellent agreement is found. We also discuss ratios R(X)equivalent to[([ X](T)-[[X](T)](av))(2)](av)/[[X](T)](av)(2), for various quantities X, to test the possible lack of self-averaging at T-c.