Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2010-11-07
Physical Review E 83, 021103 (2011)
Physics
Condensed Matter
Disordered Systems and Neural Networks
13 pages, revtex, 12 fig. incl.; fixed confusing labels, published version. For related publications, see http://www.physics
Scientific paper
10.1103/PhysRevE.83.021103
The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed-points are determined and the renormalization-group flow for certain initial conditions is analyzed. Hanoi networks combine a one-dimensional lattice structure with a hierarchy of small-world bonds to create a mix of geometric and mean-field properties. Generically, the small-world bonds result in non-universal behavior, i.e. fixed points and scaling exponents that depend on temperature and the initial choice of coupling strengths. It is shown that a diversity of different behaviors can be observed with seemingly small changes in the structure of the networks. Defining interpolating families of such networks, we find tunable transitions between regimes with power-law and certain essential singularities in the critical scaling of the correlation length, similar to the so-called inverted Berezinskii-Kosterlitz-Thouless transition previously observed only in scale-free or dense networks.
Boettcher Stefan
Brunson C. T.
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