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Rounding of first-order phase transitions and optimal cooperation in scale-free networks
M Karsai1, J-Ch Anglès d'Auriac, F Iglói
1Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2007
Summary
This study explores the ferromagnetic large-q state Potts model, revealing a phase transition from first-order to second-order in complex networks. It analyzes agent behavior and cooperation dynamics in evolving network structures.
Area of Science:
- Statistical physics
- Network science
- Complex systems
Background:
- The ferromagnetic large-q state Potts model is analyzed within complex evolving networks.
- This model is analogous to an optimal cooperation problem where agents maximize mutual benefits and project support.
Purpose of the Study:
- To investigate the phase transition properties of the Potts model in complex evolving networks.
- To characterize the behavior of agents and the nature of cooperation within these networks.
- To analyze the impact of random interactions on the phase transition.
Main Methods:
- Rigorous mathematical analysis for the homogeneous model.
- Numerical simulations on Barabási-Albert networks for random interactions.
- Characterization of finite-size transition points using shift and width exponents.
Main Results:
- A strongly first-order phase transition is rigorously shown for the homogeneous model.
- The transition becomes second-order for random interactions (benefits).
- Magnetization scales with network size N as m ~ N^(-0.66(1)).
- Finite-size transition points exhibit specific shift (1/nu'=0.26(1)) and width (1/nu'=0.18(1)) exponents.
Conclusions:
- The study elucidates the distinct phase transition behaviors of the Potts model in homogeneous versus random complex networks.
- Agent behavior is characterized by a large cooperating cluster and isolated individuals.
- The findings provide insights into cooperation dynamics and phase transitions in evolving network structures.
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