First- and second-order phase transitions in scale-free networks.

Area of Science:

• Statistical physics
• Complex networks
• Condensed matter physics

Background:

• Ferromagnetic lattice models exhibit phase transitions.
• Scale-free networks possess unique topological properties.
• Understanding phase transitions on complex networks is crucial.

Purpose of the Study:

• Investigate first- and second-order phase transitions in ferromagnetic lattice models.
• Analyze the impact of scale-free network topology (degree exponent gamma) on phase transitions.
• Examine the q-state Potts model as a representative case.

Main Methods:

• Application of the Weiss molecular-field approximation.
• Derivation of a general self-consistency relation.
• Analysis of phase diagrams based on the degree exponent gamma.

Main Results:

• Identified three distinct regimes in the phase diagram based on gamma.
• Observed that first-order transitions soften as gamma decreases.
• Found that critical singularities of second-order transitions are dependent on gamma.

Conclusions:

• The degree exponent gamma significantly influences ferromagnetic phase transitions on scale-free networks.
• The derived self-consistency relation provides insights into critical phenomena.
• Results highlight the interplay between network structure and magnetic ordering.