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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We use two-dimensional Poissonian random lattices of Voronoi/ Delaunay type to study the e ect of quenched coordination number randomness on the nature of the phase transition in the eight-state Potts model, which is of rst order on regular lattices. >From extensive Monte Carlo simulations we obtain strong evidence that the phase transition remains rst order for this type of quenched randomness. Our result is in striking contrast to a recent Monte Carlo study of quenched bond randomness for which the order of the phase transition changes from rst to second order.

We use the single-cluster Monte Carlo update algorithm to simulate the Ising model on two-dimensional Poissonian random lattices of Delaunay type with up to 80 000 sites. By applying reweighting techniques and finite-size scaling analyses to time-series data near criticality, we obtain unambiguous support that the critical exponents for the random lattice agree with the exactly known exponents for regular lattices, i.e., that (lattice) universality holds for the two-dimensional Ising model. *

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128 000 ≈ 50 3 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and φ 4 field theory on three-dimensional regular cubic lattices.

The Gonihedric Ising model is a particular case of the class of models defined by Savvidy and Wegner intended as discrete versions of string theories on cubic lattices. In this paper we perform a high statistics analysis of the phase transition exhibited by the 3d Gonihedric Ising model with k = 0 in the light of a set of recently stated scaling laws applicable to first order phase transitions with fixed boundary conditions. Even though qualitative evidence was presented in a previous paper to support the existence of a first order phase transition at k = 0, only now are we capable of pinpointing the transition inverse temperature at β c = 0.54757(63) and of checking the scaling of standard observables.