We report a fairly detailed finite-size scaling analysis of the firstorder phase transition in the three-dimensional 3-state Potts model on cubic lattices with emphasis on recently introduced quantities whose infinite-volume extrapolations are governed only by exponentially small terms. In these quantities no asymptotic power series in the inverse volume are involved which complicate the finite-size scaling behaviour of standard observables related to the specific-heat maxima or Binderparameter minima. Introduced initially for strong first-order phase transitions in q-state Potts models with "large enough" q, the new techniques prove to be surprisingly accurate for a q value as small as 3. On the basis of the high-precision Monte Carlo data of Alves et al. [Phys. Rev. B43 (1991) 5846], this leads to a refined estimate of β t = 0.550 565(10) for the infinite-volume transition point.

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We have performed Monte Carlo simulations for the three-dimensional Ising model. Using histogram techniques, we calculate the density of states on L block lattices up to size L =14. Statistical jackknife methods are employed to perform a thorough error analysis. We obtain high-precision estimates for the leading zeros of the partition function, which, using finite-size scaling, translate into v=0. 6285+0.0019. Along a different line of approach following recent work in lattice-gauge theories, we accurately determine the mass gap m = I/g (g correlation length) for cylindrical L'L, lattices (with L, =256 and L up to 12). The finite-size-scaling analysis of the mass-gap data leads to v =0.6321%0.0019.

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