Three-dimensional randomly dilute Ising model: Monte Carlo results



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Calabrese, Paquale and Martín Mayor, Víctor and Pelissetto, Andrea and Vicari, Ettore (2003) Three-dimensional randomly dilute Ising model: Monte Carlo results. Physical review E, 68 (3 (2)). ISSN 1539-3755

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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

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© 2003 The American Physical Society. V.M.-M. was partly supported by MCyT (Spain), Project Nos. FPA2001-1813 and FPA2000-0956. The numerical computations were performed at the PC Cluster at the University of Pisa. We thank Maurizio Davini for his indispensable technical assistance.

Uncontrolled Keywords:Replica-symmetry-breaking; Ranormalization-group theory; Critical disordered-systems; Symanzik beta-function; Critical exponents; Critical-behavior; Random ferromagnet; Universality class; 3 dimensions; Sigma-model.
Subjects:Sciences > Physics > Physics-Mathematical models
ID Code:46433
Deposited On:09 Mar 2018 09:30
Last Modified:09 Mar 2018 09:30

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