Volume 110, Number 2, April 2015
|Number of page(s)||6|
|Section||Condensed Matter: Structural, Mechanical and Thermal Properties|
|Published online||11 May 2015|
Classification of critical phenomena in hierarchical small-world networks
Department of Physics, Emory University - Atlanta, GA 30322, USA
Received: 3 January 2015
Accepted: 20 April 2015
A classification of critical behavior is provided in systems for which the renormalization group equations are control-parameter dependent. It describes phase transitions in networks with a recursive, hierarchical structure but appears to apply also to a wider class of systems, such as conformal field theories. Although these transitions generally do not exhibit universality, three distinct regimes of characteristic critical behavior can be discerned that combine an unusual mixture of finite- and infinite-order transitions. In the spirit of Landau's description of a phase transition, the problem can be reduced to the local analysis of a cubic recursion equation, here, for the renormalization group flow of some generalized coupling. Among other insights, this theory explains the often-noted prevalence of the so-called inverted Berezinskii-Kosterlitz-Thouless transitions in complex networks. As a demonstration, a one-parameter family of Ising models on hierarchical networks is considered.
PACS: 64.60.ae – Renormalization-group theory / 05.50.+q – Lattice theory and statistics (Ising, Potts, etc.) / 05.10.Cc – Renormalization group methods
© EPLA, 2015
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.