STRUCTURE OF 2-DIMENSIONAL SANDPILE .1. HEIGHT PROBABILITIES

被引：125
作者：
PRIEZZHEV, VB
机构：
[1] Laboratory of theoretical Physics, Joint Institute for Nuclear Research, Dubna
来源：
JOURNAL OF STATISTICAL PHYSICS | 1994年 / 74卷 / 5-6期
关键词：
SELF-ORGANIZED CRITICALITY; SANDPILES; SPANNING TREES; HEIGHT PROBABILITIES;
D O I：
10.1007/BF02188212
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
The height probabilities of the two-dimensional Abelian sandpile model are the fractional numbers of lattice sites having heights 1, 2, 3, 4. A combinatorial method for evaluation of these quantities is proposed. The method is based on mapping the set of allowed sandpile configurations onto the set of spanning trees covering a given lattice. Exact analytical expressions for all probabilities are obtained.
引用
收藏
页码：955 / 979
页数：25
相关论文
共 24 条
[1]  
[Anonymous], 1964, PRINCIPLES RANDOM WA, DOI DOI 10.1007/978-1-4757-4229-9
[2]   SELF-ORGANIZED CRITICALITY [J].
BAK, P ;
TANG, C ;
WIESENFELD, K .
PHYSICAL REVIEW A, 1988, 38 (01) :364-374
[3]   SELF-ORGANIZED CRITICALITY - AN EXPLANATION OF 1/F NOISE [J].
BAK, P ;
TANG, C ;
WIESENFELD, K .
PHYSICAL REVIEW LETTERS, 1987, 59 (04) :381-384
[4]  
Baxter R. J., 2007, EXACTLY SOLVED MODEL
[5]   PROPERTIES OF EARTHQUAKES GENERATED BY FAULT DYNAMICS [J].
CARLSON, JM ;
LANGER, JS .
PHYSICAL REVIEW LETTERS, 1989, 62 (22) :2632-2635
[6]   MAGNETIC DOMAIN PATTERNS AS SELF-ORGANIZING CRITICAL SYSTEMS [J].
CHE, XD ;
SUHL, H .
PHYSICAL REVIEW LETTERS, 1990, 64 (14) :1670-1673
[7]   SELF-ORGANIZED CRITICALITY IN A CRACK-PROPAGATION MODEL OF EARTHQUAKES [J].
CHEN, K ;
BAK, P ;
OBUKHOV, SP .
PHYSICAL REVIEW A, 1991, 43 (02) :625-630
[8]   SELF-ORGANIZED CRITICAL STATE OF SANDPILE AUTOMATON MODELS [J].
DHAR, D .
PHYSICAL REVIEW LETTERS, 1990, 64 (14) :1613-1616
[9]   LOW-FREQUENCY FLUCTUATIONS IN SOLIDS - 1-F NOISE [J].
DUTTA, P ;
HORN, PM .
REVIEWS OF MODERN PHYSICS, 1981, 53 (03) :497-516
[10]  
ERZAN A, 1990, PREPRINT ICTP
123