### Abstract

Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent (Formula presented) and the sample average of physical quantities at each (Formula presented) systematically. Using the finite-size scaling (FSS) analysis for (Formula presented) we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature (Formula presented) Its variance shows the power-law L dependence, (Formula presented) and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent (Formula presented) we show that the 2D site-diluted Ising model exhibits weak self-averaging.

Original language | English |
---|---|

Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 64 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2001 Jan 1 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*64*(3). https://doi.org/10.1103/PhysRevE.64.036114

**Crossover and self-averaging in the two-dimensional site-diluted Ising model : Application of probability-changing cluster algorithm.** / Tomita, Yusuke; Okabe, Yutaka.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 64, no. 3. https://doi.org/10.1103/PhysRevE.64.036114

}

TY - JOUR

T1 - Crossover and self-averaging in the two-dimensional site-diluted Ising model

T2 - Application of probability-changing cluster algorithm

AU - Tomita, Yusuke

AU - Okabe, Yutaka

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent (Formula presented) and the sample average of physical quantities at each (Formula presented) systematically. Using the finite-size scaling (FSS) analysis for (Formula presented) we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature (Formula presented) Its variance shows the power-law L dependence, (Formula presented) and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent (Formula presented) we show that the 2D site-diluted Ising model exhibits weak self-averaging.

AB - Using the newly proposed probability-changing cluster (PCC) Monte Carlo algorithm, we simulate the two-dimensional (2D) site-diluted Ising model. Since we can tune the critical point of each random sample automatically with the PCC algorithm, we succeed in studying the sample-dependent (Formula presented) and the sample average of physical quantities at each (Formula presented) systematically. Using the finite-size scaling (FSS) analysis for (Formula presented) we discuss the importance of corrections to FSS both in the strong-dilution and weak-dilution regions. The critical phenomena of the 2D site-diluted Ising model are shown to be controlled by the pure fixed point. The crossover from the percolation fixed point to the pure Ising fixed point with the system size is explicitly demonstrated by the study of the Binder parameter. We also study the distribution of critical temperature (Formula presented) Its variance shows the power-law L dependence, (Formula presented) and the estimate of the exponent n is consistent with the prediction of Aharony and Harris [Phys. Rev. Lett. 77, 3700 (1996)]. Calculating the relative variance of critical magnetization at the sample-dependent (Formula presented) we show that the 2D site-diluted Ising model exhibits weak self-averaging.

UR - http://www.scopus.com/inward/record.url?scp=85035259145&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035259145&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.64.036114

DO - 10.1103/PhysRevE.64.036114

M3 - Article

VL - 64

JO - Physical review. E

JF - Physical review. E

SN - 1539-3755

IS - 3

ER -