title: Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network.
abstract: 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.
authors.affiliation: Service de Physique Théorique, CNRS CEA-Saclay, 91191 Gif-sur-Yvette, France. michel.bauer@cea.fr
authors.forename: M
authors.initials: M
authors.lastname: Bauer
authors.forename: S
authors.initials: S
authors.lastname: Coulomb
authors.forename: S N
authors.initials: SN
authors.lastname: Dorogovtsev