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Published on: February 25, 2015
Nucleation in scale-free networks.
Hanshuang Chen1, Chuansheng Shen, Zhonghuai Hou
1Hefei National Laboratory for Physical Sciences at Microscales and Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, China.
Summary
Network topology significantly impacts Ising model nucleation. Homogeneous nucleation is limited in large networks, while targeted impurities greatly enhance heterogeneous nucleation rates, offering insights into phase transitions in complex systems.
Area of Science:
- Statistical Physics
- Complex Networks
- Computational Physics
Background:
- The Ising model is a fundamental tool for studying phase transitions.
- Network topology can profoundly influence system dynamics.
- Understanding nucleation is crucial for phase transition kinetics.
Purpose of the Study:
- Investigate how network topology affects Ising model nucleation dynamics.
- Quantify the influence of network structure on nucleation rates and pathways.
- Compare homogeneous and heterogeneous nucleation in scale-free networks.
Main Methods:
- Utilized the forward flux sampling method for nucleation dynamics simulation.
- Employed scale-free networks with power-law degree distributions (exponent γ).
- Analyzed homogeneous and heterogeneous nucleation with varying impurity configurations.
Main Results:
- Homogeneous nucleation clusters grow from low-degree nodes, with size following a power law.
- Nucleation rate (R{Hom}) decays exponentially with network size; critical nucleus size increases linearly.
- Targeted impurities enhance heterogeneous nucleation rate (R{Het}) more than random impurities.
- Logarithmic ratio of heterogeneous to homogeneous nucleation rates scales with impurity number (w) differently for targeted and random cases.
Conclusions:
- Homogeneous nucleation is less relevant in the thermodynamic limit due to exponential decay of nucleation rate with network size.
- Targeted impurity placement offers a significantly more effective strategy for enhancing heterogeneous nucleation.
- Simulation results are qualitatively supported by mean-field analysis, highlighting the role of network topology.
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