2005/01/31 by M. Bauer, Michel Bauer, S. Coulomb +3 · 3 citations
Mathematics · Physics and Astronomy · #Complex Network Analysis Techniques #Opinion Dynamics and Social Influence #Theoretical and Computational Physics #cond-mat.stat-mech #hep-lat #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevlett.94.200602
published as Phys.Rev.Lett. 94 (2005) 200602; Erratum-ibid. 96 (2006) 109901 · 5 pages, 2 figures. We have added a note indicating that the infinite order phase transition in the effective model we arrived at was discovered in the work: O. Costin, R.D. Costin and C.P. Grunfeld, J. Stat. Phys. 59, 1531 (1990). Appropriate references to the papers of 90s have been added
openalex publication_date 2005/05/25 · arxiv created 2006/02/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the ferromagnetic Ising model on a highly inhomogeneous network created by a growth process. We find that the phase transition in this system is characterized by the Berezinskii-Kosterlitz-Thouless singularity, although critical fluctuations are absent and the mean-field description is exact. Below this infinite order transition, the magnetization behaves as exp((-const/square root of(Tc-T)). We show that the critical point separates the phase with the power-law distribution of the linear response to a local field and the phase where this distribution rapidly decreases. We suggest that this phase transition occurs in a wide range of cooperative models with a strong infinite-range inhomogeneity.