Tensor Renormalization Group: Local Magnetizations, Correlation Functions, and Phase Diagrams of Systems with Quenched Randomness

The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched...

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Bibliographic Details
Published inarXiv.org
Main Authors Güven, Can, Hinczewski, Michael, Berker, A Nihat
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.06.2011
Subjects
Dilution
Ising model
Mathematical analysis
Percolation
Phase diagrams
Phase transitions
Physics - Disordered Systems and Neural Networks
Physics - Statistical Mechanics
Quenching
Randomness
Tensors
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Summary:The tensor renormalization-group method, developed by Levin and Nave, brings systematic improvability to the position-space renormalization-group method and yields essentially exact results for phase diagrams and entire thermodynamic functions. The method, previously used on systems with no quenched randomness, is extended in this study to systems with quenched randomness. Local magnetizations and correlation functions as a function of spin separation are calculated as tensor products subject to renormalization-group transformation. Phase diagrams are extracted from the long-distance behavior of the correlation functions. The approach is illustrated with the quenched bond-diluted Ising model on the triangular lattice. An accurate phase diagram is obtained in temperature and bond-dilution probability, for the entire temperature range down to the percolation threshold at zero temperature.
ISSN:2331-8422
DOI:10.48550/arxiv.1009.5517