Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

Details Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder Infinitely Robust Order and Local Order-Parameter Tulips in Apollonian Networks with Quenched Disorder

2008-11-20

arxiv.org/abs/0811.3437v2

Phys. Rev. E 79, 061120 (2009)

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, 4 figures; updated to reflect minor changes in published version

Scientific paper

10.1103/PhysRevE.79.061120

For a variety of quenched random spin systems on an Apollonian network, including ferromagnetic and antiferromagnetic bond percolation and the Ising spin glass, we find the persistence of ordered phases up to infinite temperature over the entire range of disorder. We develop a renormalization-group technique that yields highly detailed information, including the exact distributions of local magnetizations and local spin-glass order parameters, which turn out to exhibit, as function of temperature, complex and distinctive tulip patterns.

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