RENORMALIZATION GROUP-APPROACH FOR 2-DIMENSIONAL PERCOLATING SYSTEMS - HONEYCOMB BOND LATTICE AND KAGOME LATTICE

被引：5

作者：

MURASE, C ^{[1
]}

YUGE, Y ^{[1
]}

机构：

[1] UNIV TSUKUBA,INST AGR ENGN,SAKURA,IBARAKI 30031,JAPAN

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1979年 / 12卷 / 09期

关键词：

D O I：

10.1088/0305-4470/12/9/021

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A renormalisation group approach to two-dimensional percolation problems on the honeycomb lattice (bond) and the Kagome lattice (site and bond) is developed using a scaling transformation in real space. A finite cluster approach, called the electrode method, gives the location of the fixed point p*, the eigenvalue lambda and the correlation length critical exponent nu ; the results are p*=0.6308, lambda =1.669 and nu =1.353 for both the honeycomb lattice (bond) and the Kagome lattice (site), and p*=0.4697, lambda =1.577 and nu =1.522 for the Kagome lattice (bond). The fixed point p* for the honeycomb lattice (bond) and the Kagome lattice (site) is in good agreement with the exact critical percolation probability obtained by Sykes and Essam (1964).

引用

页码：1541 / 1546

页数：6

共 11 条

[1]

DEAN P, 1963, P CAMB PHILOS SOC, V59, P397

[2] SERIES EXPANSION STUDY OF PAIR CONNECTEDNESS IN BOND PERCOLATION MODELS [J].

DUNN, AG ;

ESSAM, JW ;

RITCHIE, DS .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1975, 8 (24) :4219-4235

[3] SOME CLUSTER SIZE AND PERCOLATION PROBLEMS [J].

FISHER, ME ;

ESSAM, JW .

JOURNAL OF MATHEMATICAL PHYSICS, 1961, 2 (04) :609-&

[4] PERCOLATION PROCESSES IN 2 DIMENSIONS .5. EXPONENT DELTA-P AND SCALING THEORY [J].

GAUNT, DS ;

SYKES, MF .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1976, 9 (07) :1109-1116

[5] RENORMALIZATION-GROUP APPROACH TO PERCOLATION PROBLEMS [J].

HARRIS, AB ;

LUBENSKY, TC ;

HOLCOMB, WK ;

DASGUPTA, C .

PHYSICAL REVIEW LETTERS, 1975, 35 (06) :327-330

[6]

Kadanoff L.P., 1966, PHYSICS, V2, P263, DOI [DOI 10.1103/PHYSICSPHYSIQUEFIZIKA.2.263, 10.1103/PhysicsPhysiqueFizika.2.263]

[7] RENORMALIZATION GROUP APPROACH FOR PERCOLATION CONDUCTIVITY [J].

STINCHCOMBE, RB ;

WATSON, BP .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1976, 9 (17) :3221-3247

[8]

SYKES MF, 1964, J MATH PHYS, V5, P117

[9] RENORMALIZATION GROUP-THEORY FOR PERCOLATION PROBLEMS [J].

YOUNG, AP ;

STINCHCOMBE, RB .

JOURNAL OF PHYSICS C-SOLID STATE PHYSICS, 1975, 8 (23) :L535-L540

[10] RENORMALIZATION-GROUP APPROACH FOR CRITICAL PERCOLATION BEHAVIOR IN 2 DIMENSIONS [J].

YUGE, Y .

PHYSICAL REVIEW B, 1978, 18 (03) :1514-1517

← 1 2 →