Exact finite-size scaling for the random-matrix representation of bond percolation on square lattice

被引:4
|
作者
Malekan, Azadeh [1 ]
Saber, Sina [1 ]
Saberi, Abbas Ali [1 ,2 ]
机构
[1] Univ Tehran, Dept Phys, POB 14395-547, Tehran, Iran
[2] Univ Cologne, Inst Theoret Phys, Zulpicher Str 77, D-50937 Cologne, Germany
关键词
LEVEL;
D O I
10.1063/5.0079323
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页数:7
相关论文
共 50 条
  • [41] The finite-size properties of the square lattice quantum Heisenberg antiferromagnet
    Song, Y
    MODERN PHYSICS LETTERS B, 2001, 15 (02): : 61 - 68
  • [42] LATTICE SHAPES AND SCALING FUNCTIONS FOR BOND RANDOM PERCOLATION ON HONEYCOMB LATTICES
    HU, CK
    CHEN, JA
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (03): : L73 - L78
  • [43] Finite-size scaling of branch-points in lattice models
    Williams, NO
    Lavis, DA
    PHYSICS LETTERS A, 1996, 217 (4-5) : 275 - 279
  • [44] Finite-size scaling of the quark condensate in quenched lattice QCD
    Hernández, P
    Jansen, K
    Lellouch, L
    PHYSICS LETTERS B, 1999, 469 (1-4) : 198 - 204
  • [45] Finite-size corrections and scaling for the dimer model on the checkerboard lattice
    Izmailian, Nickolay Sh.
    Wu, Ming-Chya
    Hu, Chin-Kun
    PHYSICAL REVIEW E, 2016, 94 (05)
  • [46] Finite-size scaling characterization of the ±J diluted Ising lattice
    Ramirez-Pastor, AJ
    Nieto, E
    Contreras, S
    Vogel, EE
    REVISTA MEXICANA DE FISICA, 1998, 44 : 89 - 92
  • [47] Finite-size scaling analysis of percolation in three-dimensional correlated binary Markov chain random fields
    Harter, T
    PHYSICAL REVIEW E, 2005, 72 (02):
  • [48] Finite-size scaling in random K-satisfiability problems
    Lee, Sang Hoon
    Ha, Meesoon
    Jeon, Chanil
    Jeong, Hawoong
    PHYSICAL REVIEW E, 2010, 82 (06):
  • [49] Phase coexistence and finite-size scaling in random combinatorial problems
    Leone, M
    Ricci-Tersenghi, F
    Zecchina, R
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (22): : 4615 - 4626
  • [50] Universal finite-size scaling functions with exact nonuniversal metric factors
    Wu, MC
    Hu, CK
    Izmailian, NS
    PHYSICAL REVIEW E, 2003, 67 (06):