The 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 $L\le 256$. 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 $R^+_ξ= 0.2885(15)$.

34 pages, 7 figs, few corrections