Journal
JOURNAL OF STATISTICAL PHYSICS
Volume 155, Issue 5, Pages 909-931Publisher
SPRINGER
DOI: 10.1007/s10955-014-0977-z
Keywords
Hierarchical lattice; Renormalization group; Critical behavior; Migdal-Kadanoff; Ferromagnet; Spin-glass; Ising model; Blume-Emery-Griffiths model
Categories
Funding
- European Union [290038]
- NETADIS
- Italian MIUR under the Basic Research Investigation Fund FIRB [RBFR08M3P4]
- PRIN [2010HXAW77-008]
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Renormalization group based on the Migdal-Kadanoff bond removal approach is often considered a simple and valuable tool to understand the critical behavior of complicated statistical mechanical models. In presence of quenched disorder, however, predictions obtained with the Migdal-Kadanoff bond removal approach quite often fail to quantitatively and qualitatively reproduce critical properties obtained in the mean-field approximation or by numerical simulations in finite dimensions. In an attempt to overcome this limitation we analyze the behavior of Ising and Blume-Emery-Griffiths models on more structured hierarchical lattices. We find that, apart from some exceptions, the failure is not limited to Midgal-Kadanoff cells but originates right from the hierarchization of Bravais lattices on small cells, and shows up also when in-cell loops are considered.
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