open access

https://hdl.handle.net/2115/50284

Criticality governed by the stable renormalization fixed point of the Ising model in the hierarchical small-world network

英語

2012-09

American Physical Society

Physical Review E

86(3)

030102

We study the Ising model in a hierarchical small-world network by 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 of 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 is 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 upon approaching the transition point.

学術雑誌論文

Version of Record

©2012 American Physical Society

1539-3755