2021/12/06 by Van Hao Can, Cristian Giardinà, Can, Van Hao +5
Physics and Astronomy · #Complex Network Analysis Techniques #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Probability (math.PR) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2112.03068
openalex publication_date 2021/12/06 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We consider spin models on complex networks frequently used to model social and technological systems. We study the annealed ferromagnetic Ising model for random networks with either independent edges (Erdős-Rényi), or with prescribed degree distributions (configuration model). Contrary to many physical models, the annealed setting is poorly understood and behaves quite differently than the quenched system. In annealed networks with a fluctuating number of edges, the Ising model changes the degree distribution, an aspect previously ignored. For random networks with Poissonian degrees, this gives rise to three distinct annealed critical temperatures depending on the precise model choice, only one of which reproduces the quenched one. In particular, two of these annealed critical temperatures are finite even when the quenched one is infinite, since then the annealed graph creates a giant component for all sufficiently small temperatures. We see that the critical exponents in the configuration model with deterministic degrees are the same as the quenched ones, which are the mean-field exponents if the degree distribution has finite fourth moment, and power-law-dependent critical exponents otherwise. Remarkably, the annealing for the configuration model with random i.i.d. degrees washes away the universality class with power-law critical exponents.