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Comparison of cluster algorithms for the bond-diluted Ising model.

Arnold H Kole1, Gerard T Barkema2, Lars Fritz3

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The Wolff cluster algorithm is inefficient for the bond-diluted Ising model due to isolated spins, while the Swendsen-Wang algorithm remains efficient. This study compares their performance, revealing significant differences in correlation times.

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Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Condensed Matter Physics

Background:

  • Monte Carlo cluster algorithms are widely used for studying the Ising model near critical temperatures.
  • The efficiency of these algorithms in the bond-diluted Ising model is not fully understood.

Purpose of the Study:

  • To compare the performance of Wolff and Swendsen-Wang cluster algorithms for the 2D bond-diluted Ising model.
  • To analyze how correlation times scale with system size for these algorithms.

Main Methods:

  • Comparison of correlation times (τ_w and τ_sw) for Wolff and Swendsen-Wang algorithms.
  • Analysis of scaling with system size (L) for the 2D bond-diluted Ising model.
  • Theoretical lower bound derivation for Wolff algorithm's correlation time.

Main Results:

  • The Wolff algorithm exhibits significantly longer correlation times in the diluted model compared to the pure Ising model.
  • Isolated spins cause the Wolff algorithm's correlation time to scale as L^z_w, with z_w ≈ 1.75.
  • The Swendsen-Wang algorithm shows shorter correlation times, even faster than in the pure Ising model, with a dynamical exponent z_sw = 0.09(4) at p=0.6.

Conclusions:

  • The efficiency of cluster algorithms is highly dependent on the specific model, with the Wolff algorithm underperforming in the bond-diluted Ising model.
  • The Swendsen-Wang algorithm is a more suitable choice for studying the 2D bond-diluted Ising model due to its superior efficiency.