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

TL;DR

This paper investigates phase transitions in ferromagnetic models on scale-free networks, revealing how the degree exponent influences the nature and critical behavior of these transitions.

Contribution

It derives a general self-consistency relation for the $q$-state Potts model on scale-free networks, identifying three regimes of phase behavior based on the degree exponent.

Findings

Three distinct phase diagram regimes depending on $mma$

First-order transitions become softer as $mma$ decreases

Critical singularities at second-order transitions depend on $mma$

Abstract

We study first- and second-order phase transitions of ferromagnetic lattice models on scale-free networks, with a degree exponent $\gamma$. Using the example of the $q$-state Potts model we derive a general self-consistency relation within the frame of the Weiss molecular-field approximation, which presumably leads to exact critical singularities. Depending on the value of $\gamma$, we have found three different regimes of the phase diagram. As a general trend first-order transitions soften with decreasing $\gamma$ and the critical singularities at the second-order transitions are $\gamma$-dependent.