Heterogeneous network topology induces the Widom line.

Abstract

The Widom line, initially identified as a crossover line between liquidlike and gaslike behavior in water and supercritical fluids, separates these two types of behavior. Here, we show that an analogous line arises in spin models on scale-free networks as a consequence of degree heterogeneity, which we analyze using the annealed network approximation. For the Ashkin-Teller and invisible Potts models, the Widom line exists within a finite range of the degree exponent. It separates two distinct ordered regimes-distributed spin alignment and hub-dominant alignment-while also giving rise to a supercritical-like state where the two alignments become indistinguishable. These results demonstrate that degree heterogeneity alone can generate mesoscopic crossovers beyond conventional phase-transition theory, opening new directions for understanding and controlling collective dynamics in complex networks.