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

摘要: The p-state mean-field Potts glass with bimodal bond distribution (±J) is studied by Monte Carlo simulations, both for p = 3 and 6 states, system sizes from N 5 to 120 spins, considering particularly the finite-size scaling behavior at exactly known transition temperature T c. It shown that moments q (k) of spin-glass order parameter satisfy a simple behavior, $$q^{(k)} \alpha N^{--k/3} \tilde f_k \{ N^{1/3} (1--T/T_c )\} ,{\text{ }}k 1,2,3,...,\tilde $$ being appropriate function T temperature. Also specific heat maxima have similar $$c_V^{\max } {\text{ }}const--N^{--1/3} , while magnetization scale as $$m^{(k)} N^{--k/2} . approach positions T max these T c → ∞ nonmonotonic. For results are compatible first-order transition, (q jump)k but since q jump rather small, ∝ N -k/3 also data. Thus no firm conclusions on can be drawn. c V max behave qualitatively in same way 3, consistent prediction there latent heat. A speculative phenomenological discussion such transitions given. small (N ≤15 ≤ 12 6) data compared exact partition calculations, excellent agreement found. We discuss ratios $$R_x \equiv [(\langle X\rangle _T - [\langle ]_{{\text{av}}} )^2 /[\langle ]_{{\text{av}}}^2 various quantities X, test possible lack self-averaging