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Metastable configurations of small-world networks
R Heylen1, N S Skantzos, J Busquets Blanco
1Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven, Belgium. rob.heylen@fys.kuleuven.be
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 21, 2006
Summary
We calculated metastable configurations in Ising small-world networks. A jump in entropy was found at the structural crossover between small-world and Poisson random graphs.
Area of Science:
- Statistical physics
- Network science
- Complex systems
Background:
- Ising models are fundamental in statistical mechanics.
- Small-world networks exhibit unique topological properties.
- Understanding network phase transitions is crucial.
Purpose of the Study:
- To determine the number of metastable configurations in a novel network model.
- To investigate the impact of network structure on system entropy.
- To analyze ground state degeneracy and entropy differences.
Main Methods:
- Replicated transfer-matrix techniques were employed.
- Analysis of metastable states and ground state degeneracy.
- Examination of entropy for ferromagnetic and bond-disordered couplings.
Main Results:
- A distinct jump in metastable configuration entropy was observed.
- This jump occurs precisely at the small-world to Poisson graph crossover.
- Differences in entropy were quantified for various coupling types.
Conclusions:
- Network topology significantly influences thermodynamic properties.
- The crossover point reveals critical changes in system behavior.
- The findings provide insights into phase transitions in complex networks.
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