ENUMERATING 2D PERCOLATION SERIES BY THE FINITE-LATTICE METHOD - THEORY

被引:24
作者
CONWAY, A
机构
[1] Dept. of Math., Melbourne Univ., Parkville, Vic.
来源
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1995年 / 28卷 / 02期
关键词
D O I
10.1088/0305-4470/28/2/011
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
This paper describes a transfer-matrix algorithm for enumeration of series of interest in percolation on the square lattice. It allows efficient generation of both low-temperature and high-temperature expansions, as well as the combinatorially interesting enumeration of undirected animals by area or perimeter, with moments of the other property.
引用
收藏
页码:335 / 349
页数:15
相关论文
共 17 条
[1]   SERIES STUDY OF PERCOLATION MOMENTS IN GENERAL DIMENSION [J].
ADLER, J ;
MEIR, Y ;
AHARONY, A ;
HARRIS, AB .
PHYSICAL REVIEW B, 1990, 41 (13) :9183-9206
[2]  
BETREMA J, 1991, SERIES FORMELLES COM, P85
[3]   ENUMERATION OF SELF-AVOIDING TRAILS ON A SQUARE LATTICE USING A TRANSFER-MATRIX TECHNIQUE [J].
CONWAY, AR ;
GUTTMANN, AJ .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (07) :1535-1552
[4]  
CONWAY AR, 1994, UNPUB J PHYS A
[5]   POLYOMINOES AND ANIMALS - SOME RECENT RESULTS [J].
DELEST, M .
JOURNAL OF MATHEMATICAL CHEMISTRY, 1991, 8 (1-3) :3-18
[6]   SERIES STUDY OF RANDOM PERCOLATION IN 3 DIMENSIONS [J].
GAUNT, DS ;
SYKES, MF .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1983, 16 (04) :783-799
[7]   ON THE NUMBER OF LATTICE ANIMALS EMBEDDABLE IN THE SQUARE LATTICE [J].
GUTTMANN, AJ .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1982, 15 (06) :1987-1990
[8]   THE IMPACT OF LARGE-SCALE COMPUTING ON LATTICE STATISTICS [J].
MARTIN, JL .
JOURNAL OF STATISTICAL PHYSICS, 1990, 58 (3-4) :749-774
[9]   LATTICE ANIMALS - A FAST ENUMERATION ALGORITHM AND NEW PERIMETER POLYNOMIALS [J].
MERTENS, S .
JOURNAL OF STATISTICAL PHYSICS, 1990, 58 (5-6) :1095-1108
[10]  
REDELMEIER DH, 1981, DISCRETE MATH, V36, P191, DOI 10.1016/0012-365X(81)90237-5