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 slates, for system sizes from N = 5 to N = 120 spins, considering particularly the finite-size scaling behavior at the exactly known glass transition temperature T-c. It is shown that for p=3 the moments g((k)) of the 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 the temperature. Also the specific heat maxima have a similar behavior, c(V)(max) proportional to const - N-1/3, while moments of the magnetization scale as m((k)) proportional to N-k/2. The approach of the positions T,,, of these specific heat maxima to T-c as N --> infinity is nonmonotonic. For p=6 the results are compatible with a first-order transition, q((k)) --> (q(jump))(k) as N---> infinity, but since the order parameter q(jump) at T-c is rather small, a behavior q((k)) proportional 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 latent heat. A speculative phenomenological discussion of finite-size scaling for such transitions is given. For small N (N less than or equal to 15 for p = 3, N less than or equal to 12 for p = 6) the Monte Carlo data are compared to exact partition function calculations, and excellent 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.