Phase transition with the Berezinskii-Kosterlitz-Thouless singularity in the Ising model on a growing network.
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.
Bauer
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Service de Physique Théorique, CNRS CEA-Saclay, 91191 Gif-sur-Yvette, France. michel.bauer@cea.fr
Coulomb
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Dorogovtsev
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