1206.5064 (Tomoaki Nogawa et al.)

Novel criticality governed by the stable renormalization fixed point of
the Ising model in the hierarchical small-world network    [PDF]

Tomoaki Nogawa, Takehisa Hasegawa, Koji Nemoto

We study the Ising model in a hierarchical small-world network by the renormalization group analysis, and find a phase transition between an ordered phase and a critical phase, which is driven by the coupling strength of the shortcut edges. Unlike ordinary phase transitions, which are related to unstable renormalization fixed points (FPs), the singularity in the ordered phase of the present model is governed by the FP that coincides with the stable FP for the ordered phase. The weak stability of the FP yields peculiar criticalities including logarithmic behavior. On the other hand, the critical phase is related to a nontrivial FP, which depends on the coupling strength and continuously connected to the ordered FP at the transition point. We show that this continuity indicates the existence of a finite correlation-length-like quantity inside the critical phase, which diverges as approaching the transition point.

View original: http://arxiv.org/abs/1206.5064