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 $\nu =0.683(3)$, $\eta =0.035(2)$, $\beta =0.3535(17)$, and $\alpha =-0.049(9)$, 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 $R_{\xi }^{+}$ that expresses the universality of the free-energy density per correlation volume. We find $R_{\xi }^{+}=0.2885(15)$.

34 pages, 7 figs, few corrections

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