2003/06/30 by P. Calabrese, Pasquale Calabrese, V. Martı́n-Mayor +5 · 1 citation
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech #hep-lat
paper · pdf · doi:10.1103/physreve.68.036136
published as Phys.Rev. E68 (2003) 036136 · 34 pages, 7 figs, few corrections
arxiv created 2003/07/30 · openalex publication_date 2003/09/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We perform a high-statistics simulation of the three-dimensional randomly dilute Ising model on cubic lattices L3 with L< or =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).