Three-dimensional randomly dilute Ising model: Monte Carlo results

Abstract

We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L^(3) with L<~256. We choose a particular value of the density, x=0.8, for which the leading scaling corrections are suppressed. We determine the critical exponents, obtaining ν=0.683(3), η=0.035(2), β=0.3535(17), and α=−0.049(9), in agreement with previous numerical simulations. We also estimate numerically the fixed-point values of the four-point zero-momentum couplings that are used in field-theoretical fixed-dimension studies. Although these results somewhat differ from those obtained using perturbative field theory, the field-theoretical estimates of the critical exponents do not change significantly if the Monte Carlo result for the fixed point is used. Finally, we determine the six-point zero-momentum couplings, relevant for the small-magnetization expansion of the equation of state, and the invariant amplitude ratio R^(+)_(ξ) that expresses the universality of the free-energy density per correlation volume. We find R^(+)_(ξ)=0.2885(15