### Abstract

We study the effect of varying strength δ of bond randomness on the phase transition of the three-dimensional Potts model for large q. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder δ> δt this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that δt is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as βt νt =0.10(2) and νt =0.67(4). We claim these exponents are q independent for sufficiently large q. In the second-order transition regime the critical exponents βt νt =0.60(2) and νt =0.73(1) are independent of the strength of disorder.

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

Article number | 026126 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 73 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*73*(2), [026126]. https://doi.org/10.1103/PhysRevE.73.026126

**Critical and tricritical singularities of the three-dimensional random-bond Potts model for large q.** / Mercaldo, M. T.; D'Auriac, J. Ch Anglès; Iglói, F.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 73, no. 2, 026126. https://doi.org/10.1103/PhysRevE.73.026126

}

TY - JOUR

T1 - Critical and tricritical singularities of the three-dimensional random-bond Potts model for large q

AU - Mercaldo, M. T.

AU - D'Auriac, J. Ch Anglès

AU - Iglói, F.

PY - 2006

Y1 - 2006

N2 - We study the effect of varying strength δ of bond randomness on the phase transition of the three-dimensional Potts model for large q. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder δ> δt this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that δt is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as βt νt =0.10(2) and νt =0.67(4). We claim these exponents are q independent for sufficiently large q. In the second-order transition regime the critical exponents βt νt =0.60(2) and νt =0.73(1) are independent of the strength of disorder.

AB - We study the effect of varying strength δ of bond randomness on the phase transition of the three-dimensional Potts model for large q. The cooperative behavior of the system is determined by large correlated domains in which the spins point in the same direction. These domains have a finite extent in the disordered phase. In the ordered phase there is a percolating cluster of correlated spins. For a sufficiently large disorder δ> δt this percolating cluster coexists with a percolating cluster of noncorrelated spins. Such a coexistence is only possible in more than two dimensions. We argue and check numerically that δt is the tricritical disorder, which separates the first- and second-order transition regimes. The tricritical exponents are estimated as βt νt =0.10(2) and νt =0.67(4). We claim these exponents are q independent for sufficiently large q. In the second-order transition regime the critical exponents βt νt =0.60(2) and νt =0.73(1) are independent of the strength of disorder.

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U2 - 10.1103/PhysRevE.73.026126

DO - 10.1103/PhysRevE.73.026126

M3 - Article

AN - SCOPUS:33644509821

VL - 73

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 2

M1 - 026126

ER -