### Abstract

We consider the ferromagnetic large- q state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: A fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barabási-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, 1 ν ′ =0.26 (1), and by a different width exponent, 1 ν′ =0.18 (1), whereas the magnetization at the transition point scales with the size of the network, N, as m∼ N-x, with x=0.66 (1).

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

Article number | 041107 |

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

Volume | 76 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 3 2007 |

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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*,

*76*(4), [041107]. https://doi.org/10.1103/PhysRevE.76.041107

**Rounding of first-order phase transitions and optimal cooperation in scale-free networks.** / Karsai, M.; D'Auriac, J. Ch Anglès; Iglói, F.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 76, no. 4, 041107. https://doi.org/10.1103/PhysRevE.76.041107

}

TY - JOUR

T1 - Rounding of first-order phase transitions and optimal cooperation in scale-free networks

AU - Karsai, M.

AU - D'Auriac, J. Ch Anglès

AU - Iglói, F.

PY - 2007/10/3

Y1 - 2007/10/3

N2 - We consider the ferromagnetic large- q state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: A fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barabási-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, 1 ν ′ =0.26 (1), and by a different width exponent, 1 ν′ =0.18 (1), whereas the magnetization at the transition point scales with the size of the network, N, as m∼ N-x, with x=0.66 (1).

AB - We consider the ferromagnetic large- q state Potts model in complex evolving networks, which is equivalent to an optimal cooperation problem, in which the agents try to optimize the total sum of pair cooperation benefits and the supports of independent projects. The agents are found to be typically of two kinds: A fraction of m (being the magnetization of the Potts model) belongs to a large cooperating cluster, whereas the others are isolated one man's projects. It is shown rigorously that the homogeneous model has a strongly first-order phase transition, which turns to second-order for random interactions (benefits), the properties of which are studied numerically on the Barabási-Albert network. The distribution of finite-size transition points is characterized by a shift exponent, 1 ν ′ =0.26 (1), and by a different width exponent, 1 ν′ =0.18 (1), whereas the magnetization at the transition point scales with the size of the network, N, as m∼ N-x, with x=0.66 (1).

UR - http://www.scopus.com/inward/record.url?scp=35248897198&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35248897198&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.76.041107

DO - 10.1103/PhysRevE.76.041107

M3 - Article

AN - SCOPUS:35248897198

VL - 76

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

M1 - 041107

ER -