Hierarchical renormalization-group study on the planar bond-percolation problem

Physica Scripta

Volumn 83, Issue 5, 2011, Pages

  Baek, Seung Ki ^a   Minnhagen, Petter ^a  

^a UMEÅ UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

BOND PERCOLATION; CRITICAL EXPONENT; HIERARCHICAL STRUCTURES; LOWER BOUNDS; PERCOLATION PROBLEMS; PLANAR LATTICE; RENORMALIZATION GROUP;

SOLVENTS;

EID: 79955833182     PISSN: 00318949     EISSN: 14024896     Source Type: Journal    
DOI: 10.1088/0031-8949/83/05/055601     Document Type: Article

References (12)

1. Stauffer D and Aharony A 2003 Introduction to Percolation Theory 2nd (London: Taylor and Francis)
2. Fortuin C M and Kasteleyn P W 1972 On the random-cluster model: I. Introduction and relation to other models Physica 57 536
3. Niemeijer Th and van Leeuwen J M J 1973 Wilson theory for spin systems on a triangular lattice Phys. Rev. Lett. 31 1411
4. Reynolds P J, Klein W and Stanley H E 1977 A real-space renormalization group for site and bond percolation J. Phys. C: Solid State Phys. 10 L167
5. Reynolds P J, Stanley H E and Klein W 1980 Large-cell Monte Carlo renormalization group for percolation Phys.Rev. B 21 1223
6. Rozenfeld H D and ben Avraham D 2007 Percolation in hierarchical scale-free nets Phys. Rev. E 75 061102
7. Boettcher S, Cook J L and Ziff R M 2009 Patch percolation on a hierarchical network with small-world bonds Phys. Rev. E 80 041115
8. Baek S K and Minnhagen P 2011 Bounds of percolation thresholds in the enhanced binary tree Physica A 390 1447
9. Minnhagen P and Baek S K 2010 Analytic results for the percolation transitions of the enhanced binary tree Phys.Rev. E 82 011113
10. Sykes M F and Essam J W 1963 Some exact critical percolation probabilities for bond and site problems in two dimensions Phys. Rev. Lett. 10 3
11. Kesten H 1980 The critical probability of bond percolation on the square lattice equals 1/2 Commun. Math. Phys. 74 41
12. den Nijs M P M 1979 A relation between the temperature exponents of the eight-vertex and q-state Potts model J.Phys. A: Math. Gen. 12 1857