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

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.