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

TL;DR

This paper studies how phase coherence develops in coupled oscillators on small-world networks, examining the effects of noise and randomness, and finds finite-temperature phase ordering with minimal shortcuts.

Contribution

It introduces analysis of phase ordering on small-world networks with nearest-neighbor edges, highlighting the impact of shortcuts and noise on coherence.

Findings

Phase ordering occurs at finite temperatures with few shortcuts.

Thermal noise and quenched randomness influence phase coherence.

The nature of the phase transition is discussed.

Abstract

We investigate global phase coherence in a system of coupled oscillators on a small-world networks constructed from a ring with nearest-neighbor edges. The effects of both thermal noise and quenched randomness on phase ordering are examined and compared with the global coherence in the corresponding \xy model without quenched randomness. It is found that in the appropriate regime phase ordering emerges at finite temperatures, even for a tiny fraction of shortcuts. Nature of the phase transition is also discussed.