Phase ordering on small-world networks with nearest-neighbor edges

Area of Science:

• Complex systems
• Statistical physics
• Network science

Background:

• Coupled oscillator systems are fundamental to understanding emergent phenomena.
• Small-world networks exhibit unique topological properties, bridging regular and random networks.
• Phase ordering and coherence are critical in various physical and biological systems.

Purpose of the Study:

• To investigate global phase coherence in coupled oscillators on small-world networks.
• To analyze the impact of thermal noise and quenched randomness on phase ordering.
• To compare coherence in networks with and without quenched randomness.

Main Methods:

• Construction of small-world networks from a ring with nearest-neighbor edges and added shortcuts.
• Simulation of coupled oscillators under thermal noise and quenched randomness.
• Analysis of phase ordering and global coherence metrics.

Main Results:

• Phase ordering emerges at finite temperatures in the appropriate regime, even with a small fraction of shortcuts.
• The presence of quenched randomness influences the nature and onset of phase ordering.
• Comparison with the XY model reveals distinct coherence behaviors.

Conclusions:

• Small-world topology facilitates global phase coherence at finite temperatures.
• Both thermal fluctuations and quenched disorder play significant roles in phase ordering dynamics.
• The study provides insights into synchronization phenomena in complex networks.