Finite size scaling study of lattice models in the three-dimensional Ising universality class

We study the spin-1/2 Ising model and the Blume-Capel model at various values of the parameter D on the simple cubic lattice. To this end we perform Monte Carlo simulations using a hybrid of the local Metropolis, the single cluster and the wall cluster algorithm. Using finite size scaling we determine the value D^=0. 656 (20) of the parameter D, where leading corrections to scaling vanish. We find =0. 832 (6) for the exponent of leading corrections to scaling. In order to compute accurate estimates of critical exponents, we construct improved observables that have a small amplitude of the leading correction for any model. Analyzing data obtained for D=0. 641 and 0. 655 on lattices of a linear size up to L=360 we obtain =0. 63002 (10) and =0. 03627 (10). We compare our results with those obtained from previous Monte Carlo simulations and high-temperature series expansions of lattice models, by using field-theoretic methods and experiments.