We investigate several three-dimensional lattice models believed to be in the Ising universality class by means of Monte Carlo methods and finite-size scaling. These models include spin-$\frac{1}{2}$ models with nearest-neighbor interactions on the simple-cubic and on the diamond lattice. For the simple cubic lattice, we also include models with third-neighbor interactions of varying strength, and some “equivalent-neighbor” models. Also included are a spin-$1$ model and a hard-core lattice gas. Separate analyses of the numerical data confirm the Ising-like critical behavior of these systems. On this basis, we analyze all these data simultaneously such that the universal parameters occur only once. This leads to an improved accuracy. The thermal, magnetic, and irrelevant exponents are determined as $y_t=1.5868\mathrm{}\left(3\right),$ $y_h=2.4816\mathrm{}\left(1\right),$ and $y_i=-0.821\left(5\right),$ respectively. The Binder ratio is estimated as $Q=〈m^2{〉}^2/〈m^4〉=0.62\mathrm{}341\left(4\right).$

• Received 25 April 2003

DOI:https://doi.org/10.1103/PhysRevE.68.036125