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Three-dimensional randomly dilute Ising model: Monte Carlo results.

Pasquale Calabrese1, Victor Martín-Mayor, Andrea Pelissetto

  • 1Scuola Normale Superiore and INFN, Piazza dei Cavalieri 7, I-56126 Pisa, Italy. calabres@df.unipi.it

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 4, 2003
PubMed
Summary

This study simulates the three-dimensional randomly dilute Ising model, determining critical exponents and couplings. Results confirm universality and refine understanding of critical phenomena in disordered magnetic systems.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • The three-dimensional randomly dilute Ising model is a key system for studying critical phenomena in disordered magnetic materials.
  • Understanding critical exponents and scaling functions is crucial for characterizing phase transitions.

Purpose of the Study:

  • To perform a high-statistics simulation of the 3D randomly dilute Ising model.
  • To accurately determine critical exponents and scaling parameters.
  • To compare numerical results with field-theoretical predictions.

Main Methods:

  • High-statistics Monte Carlo simulations on cubic lattices up to L=256.
  • Focus on a specific density (x=0.8) to suppress leading scaling corrections.
  • Numerical estimation of four-point and six-point zero-momentum couplings.

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Main Results:

  • Precise determination of critical exponents: nu=0.683(3), eta=0.035(2), beta=0.3535(17), alpha=-0.049(9).
  • Numerical estimation of fixed-point values for couplings used in field-theoretical studies.
  • Calculation of the invariant amplitude ratio R(+)(xi)=0.2885(15), confirming universality.

Conclusions:

  • The obtained critical exponents are in agreement with previous numerical simulations.
  • Field-theoretical estimates of critical exponents remain robust even when using Monte Carlo-derived fixed-point values.
  • The study provides strong evidence for the universality of the free-energy density per correlation volume in this model.