Heterogeneous Network Topology Induces the Widom Line

Abstract

The Widom line, initially identified as a crossover line between liquid-like and gas-like 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.

26 pages, 11 figures

References in corpus (28)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• The structure and function of complex networks
• Statistical physics of social dynamics
• Multilayer Networks
• The structure and dynamics of multilayer networks
• Critical phenomena in complex networks
• Networks beyond pairwise interactions: structure and dynamics
• Are biological systems poised at criticality?
• Sociophysics: A review of Galam models
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Social interactions dominate speed control in driving natural flocks toward criticality
• Mean field solution of the Ising model on a Barabasi-Albert network
• First passage time for random walks in heterogeneous networks
• Evidence for quasicritical brain dynamics
• Ising model in scale-free networks: A Monte Carlo simulation
• Transition in the supercritical state of matter: experimental evidence
• Critical behavior of the Ising model in annealed scale-free networks
• Theoretical foundations of studying criticality in the brain
• First-Order Transition to Incommensurate Phase with Broken Lattice Rotation Symmetry in Frustrated Heisenberg Model
• Origin of the mixed-order transition in multiplex networks: the Ashkin-Teller model
• Phase Transition in Potts Model with Invisible States
• Thermodynamic crossovers in supercritical fluids
• Potts Model with Invisible States: A Review
• Link overlap influences opinion dynamics on multiplex networks: spin model approach
• Potts model with invisible states on a scale-free network
• Ashkin-Teller model with antiferromagnetic four-spin interactions: Interference effect between two conflicting issues