Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices

Journal article


Dhesi, G and Ausloos, M (2016). Finite size effects in the averaged eigenvalue density of Wigner random-sign real symmetric matrices. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 93 (6). https://doi.org/10.1103/PhysRevE.93.062115
AuthorsDhesi, G and Ausloos, M
Abstract

© 2016 American Physical Society.Nowadays, strict finite size effects must be taken into account in condensed matter problems when treated through models based on lattices or graphs. On the other hand, the cases of directed bonds or links are known to be highly relevant in topics ranging from ferroelectrics to quotation networks. Combining these two points leads us to examine finite size random matrices. To obtain basic materials properties, the Green's function associated with the matrix has to be calculated. To obtain the first finite size correction, a perturbative scheme is hereby developed within the framework of the replica method. The averaged eigenvalue spectrum and the corresponding Green's function of Wigner random sign real symmetric N×N matrices to order 1/N are finally obtained analytically. Related simulation results are also presented. The agreement is excellent between the analytical formulas and finite size matrix numerical diagonalization results, confirming the correctness of the first-order finite size expression.

KeywordsMathematical Sciences; Physical Sciences; Engineering; Fluids & Plasmas
Year2016
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Journal citation93 (6)
PublisherAmerican Physical Society
ISSN1539-3755
Digital Object Identifier (DOI)https://doi.org/10.1103/PhysRevE.93.062115
Web address (URL)https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.062115
Publication dates
Print09 Jun 2016
Publication process dates
Deposited18 Jan 2017
Accepted30 Mar 2016
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Accepted author manuscript
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Open
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