We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions, which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in uncorrelated scale-free networks, where the node-degree distribution exponent λ appears to be a global variable and plays a crucial role, similar to the dimensionality d for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.
von Ferber, C., Folk, R., Holovatch, Y., Kenna, R., & Palchykov, V. (2011). Entropic equation of state and scaling functions near the critical point in uncorrelated scale-free networks. Physical Review E, 83, . https://doi.org/10.1103/PhysRevE.83.061114