Topological phase transition of a fractal spin system: The relevance of the network complexity

A new type of collective excitations, due to the topology of a complex random network that can be characterized by a fractal dimension D-F, is investigated. We show analytically that these excitations generate phase transitions due to the non-periodic topology of the D-F > 1 complex network. An Ising system, with long range interactions, is studied in detail to support the claim. The analytic treatment is possible because the evaluation of the partition function can be decomposed into closed factor loops, in spite of the architectural complexity. The removal of the infrared divergences leads to an unconventional phase transition, with spin correlations that are robust against thermal fluctuations. (C) 2016 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.