Abstract
We analyze the phase transitions that emerge from the recursive design of certain hyperbolic networks that includes, for instance, a discontinuous (“explosive”) transition in ordinary percolation. To this end, we solve the -state Potts model in the analytic continuation for noninteger with the real-space renormalization group. We find exact expressions for this one-parameter family of models that describe the dramatic transformation of the transition. In particular, this variation in shows that the discontinuous transition is generic in the regime that includes percolation. A continuous ferromagnetic transition is recovered in a singular manner only for the Ising model, . For the transition immediately transforms into an infinitely smooth order parameter of the Berezinskii-Kosterlitz-Thouless type.
- Received 7 August 2014
DOI:https://doi.org/10.1103/PhysRevE.90.052119
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