### Abstract

We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random-Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.

Original language | English |
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Number of pages | 1 |

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

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 1 2001 |

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### ASJC Scopus subject areas

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

### Cite this

**Random-bond Potts model in the large-q limit.** / Juhász, Róbert; Rieger, Heiko; Iglói, F.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 64, no. 5. https://doi.org/10.1103/PhysRevE.64.056122

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TY - JOUR

T1 - Random-bond Potts model in the large-q limit

AU - Juhász, Róbert

AU - Rieger, Heiko

AU - Iglói, F.

PY - 2001/1/1

Y1 - 2001/1/1

N2 - We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random-Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.

AB - We study the critical behavior of the q-state Potts model with random ferromagnetic couplings. Working with the cluster representation the partition sum of the model in the large-q limit is dominated by a single graph, the fractal properties of which are related to the critical singularities of the random-Potts model. The optimization problem of finding the dominant graph, is studied on the square lattice by simulated annealing and by a combinatorial algorithm. Critical exponents of the magnetization and the correlation length are estimated and conformal predictions are compared with numerical results.

UR - http://www.scopus.com/inward/record.url?scp=85035264163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85035264163&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.64.056122

DO - 10.1103/PhysRevE.64.056122

M3 - Article

AN - SCOPUS:85035264163

VL - 64

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 5

ER -