Universität zu Köln

Malekan, Azadeh, Saber, Sina and Saberi, Abbas Ali ORCID: 0000-0001-8864-4748 (2022). Exact finite-size scaling for the random-matrix representation of bond percolation on square lattice. Chaos, 32 (2). MELVILLE: AIP Publishing. ISSN 1089-7682

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Abstract

We report on the exact treatment of a random-matrix representation of a bond-percolation model on a square lattice in two dimensions with occupation probability p. The percolation problem is mapped onto a random complex matrix composed of two random real-valued matrices of elements + 1 and - 1 with probability p and 1 - p, respectively. We find that the onset of percolation transition can be detected by the emergence of power-law divergences due to the coalescence of the first two extreme eigenvalues in the thermodynamic limit. We develop a universal finite-size scaling law that fully characterizes the scaling behavior of the extreme eigenvalue's fluctuation in terms of a set of universal scaling exponents and amplitudes. We make use of the relative entropy as an index of the disparity between two distributions of the first and second-largest extreme eigenvalues to show that its minimum underlies the scaling framework. Our study may provide an inroad for developing new methods and algorithms with diverse applications in machine learning, complex systems, and statistical physics.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Malekan, Azadeh UNSPECIFIED UNSPECIFIED UNSPECIFIED Saber, Sina UNSPECIFIED UNSPECIFIED UNSPECIFIED Saberi, Abbas Ali UNSPECIFIED orcid.org/0000-0001-8864-4748 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-668347
DOI:	10.1063/5.0079323
Journal or Publication Title:	Chaos
Volume:	32
Number:	2
Date:	2022
Publisher:	AIP Publishing
Place of Publication:	MELVILLE
ISSN:	1089-7682
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language LEVEL Multiple languages Mathematics, Applied; Physics, Mathematical Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66834