Heterogeneous network topology induces the Widom line.

Area of Science:

• Statistical physics
• Network science
• Complex systems

Background:

• The Widom line traditionally describes crossovers between liquidlike and gaslike states in fluids.
• Spin models on networks exhibit complex collective behaviors influenced by network topology.

Purpose of the Study:

• To investigate the emergence of a Widom line in spin models on scale-free networks.
• To analyze the impact of degree heterogeneity on network dynamics and phase transitions.

Main Methods:

• Utilized the annealed network approximation for analysis.
• Examined the Ashkin-Teller and invisible Potts models on scale-free networks.

Main Results:

• An analogous Widom line was identified in spin models on scale-free networks.
• Degree heterogeneity was shown to be the cause of this Widom line.
• The line separates distributed spin alignment from hub-dominant alignment.
• A supercritical-like state emerged where alignments became indistinguishable.

Conclusions:

• Degree heterogeneity alone can induce mesoscopic crossovers in complex networks.
• Findings extend beyond conventional phase-transition theory.
• Opens new avenues for understanding and controlling collective dynamics in networks.