We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to be relatively large. Combining the Monte Carlo results for the hydrogen peroxide lattice with those for five other three-dimensional lattices, we obtain a set of data covering a wide range of the irrelevant temperature field. This is helpful in the determination of the parameters describing the corrections to scaling. As a consequence, new results are obtained for the universal parameters describing Ising criticality in three dimensions, with reduced error margins in comparison with earlier Monte Carlo analyses. The critical exponents describing the thermodynamic singularities are determined by the temperature renormalization exponent yt = 1.58693(9) and the magnetic renormalization exponent yh = 2.48178(5). The corrections to scaling are governed by the irrelevant exponent y1 = −0.821(5).
Recent advances in conformal field theory and critical phenomena have focused on the characterization of boundary or defects in a conformally invariant system. In this Letter, we study the critical behavior of the three-dimensional Ising universality class in the presence of a surface, realizing the ordinary, the special, and the normal universality classes. By combining high-precision Monte Carlo simulations of an improved model, where leading scaling corrections are suppressed, with a finite-size scaling analysis informed by conformal field theory, we determine unbiased, accurate estimates of universal boundary operator product expansion coefficients of experimental relevance. Furthermore, we improve the value of the scaling dimension of the surface field at the special transition by the estimate Δ ̂ σ = 0.3531 ( 3 ) .
Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent
β of the directed Ising universality class. The value of
β was conjectured to be
1413 and Monte Carlo simulation studies in the literature have repeatedly reproduced the consistent values to the conjecture. In this paper, however, we find that the conjectured value of
β is not correct. Rather, we obtain
β = 1.020(5) from different models belonging to the directed Ising class.