  Finite-size effects in the mean-field Ising spin glass and the mean-field
three-state Potts glass are investigated by Monte Carlo simulations. In the
thermodynamic limit, each model is known to exhibit a continuous phase
transition into the ordered state with a full and a one-step replica-symmetry
breaking (RSB), respectively. In the Ising case, Binder parameter g calculated
for various finite sizes remains positive at any temperature and crosses at the
transition point, while in the Potts case g develops a negative dip without
showing a crossing in the g>0 region. By contrast, non-self averaging
parameters always remain positive and show a clear crossing at the transition
temperature in both cases. Our finding suggests that care should be taken in
interpreting the numerical data of the Binder parameter, particularly when the
system exhibits a one-step-like RSB.
