### Abstract

We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values. J_{1} <J_{2}, with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip ξ_{L} for different widths of the strip L ≤ 21. The ratio of the two lengths ξ_{L}/L = A is found to approach the universal value A = 2/π for large L, independent of the dilution parameter J_{1}/J_{2}. With our method we have demonstrated with high numerical precision, that the surface correlation function of the 2D dilute Ising model is self-averaging, in the critical point conformally covariant and the corresponding decay exponent is η = 1.

Original language | English |
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Pages (from-to) | 147-152 |

Number of pages | 6 |

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

Volume | 61 |

Issue number | 1 |

Publication status | Published - Jan 2000 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

**Correlation-length-exponent relation for the two-dimensional random Ising model.** / Lajkó, Péter; Iglói, F.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 61, no. 1, pp. 147-152.

}

TY - JOUR

T1 - Correlation-length-exponent relation for the two-dimensional random Ising model

AU - Lajkó, Péter

AU - Iglói, F.

PY - 2000/1

Y1 - 2000/1

N2 - We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values. J1 <J2, with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip ξL for different widths of the strip L ≤ 21. The ratio of the two lengths ξL/L = A is found to approach the universal value A = 2/π for large L, independent of the dilution parameter J1/J2. With our method we have demonstrated with high numerical precision, that the surface correlation function of the 2D dilute Ising model is self-averaging, in the critical point conformally covariant and the corresponding decay exponent is η = 1.

AB - We consider the two-dimensional (2D) random Ising model on a diagonal strip of the square lattice, where the bonds take two values. J1 <J2, with equal probability. Using an iterative method, based on a successive application of the star-triangle transformation, we have determined at the bulk critical temperature the correlation length along the strip ξL for different widths of the strip L ≤ 21. The ratio of the two lengths ξL/L = A is found to approach the universal value A = 2/π for large L, independent of the dilution parameter J1/J2. With our method we have demonstrated with high numerical precision, that the surface correlation function of the 2D dilute Ising model is self-averaging, in the critical point conformally covariant and the corresponding decay exponent is η = 1.

UR - http://www.scopus.com/inward/record.url?scp=0004830877&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004830877&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0004830877

VL - 61

SP - 147

EP - 152

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 1

ER -