Cluster distribution in mean-field percolation: Scaling and universality

被引：6

作者：

Rudnick, J

Nakmahachalasint, P

Gaspari, G

机构：

[1] Univ Calif Los Angeles, Dept Phys, Los Angeles, CA 90095 USA

[2] Univ Calif Santa Cruz, Dept Phys, Santa Cruz, CA 95064 USA

来源：

PHYSICAL REVIEW E | 1998年 / 58卷 / 05期

关键词：

D O I：

10.1103/PhysRevE.58.5596

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

The partition function of the finite q-state Potts model in the limit q --> 1 is shown to yield a closed form for the distribution of clusters in the immediate vicinity of the percolation transition. Various important properties of the transition are manifest, including scaling behavior and the emergence of the spanning cluster. [S1063-651X(98)15311-4].

引用

页码：5596 / 5601

页数：6

共 50 条

[1] SCALING WINDOW FOR MEAN-FIELD PERCOLATION OF AVERAGES
Ding, Jian
[J]. ANNALS OF PROBABILITY, 2013, 41 (06): : 4407 - 4427
[2] FINTIE-SIZE SCALING FOR MEAN-FIELD PERCOLATION
GAVEAU, B
SCHULMAN, LS
[J]. JOURNAL OF STATISTICAL PHYSICS, 1993, 70 (3-4) : 613 - 634
[3] The mean-field scaling function of the universality class of absorbing phase transitions with a conserved field
Lübeck, S
Hucht, A
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (23): : 4853 - 4860
[4] Universality of the mean-field for the Potts model
Anirban Basak
Sumit Mukherjee
[J]. Probability Theory and Related Fields, 2017, 168 : 557 - 600
[5] Universality of the mean-field for the Potts model
Basak, Anirban
Mukherjee, Sumit
[J]. PROBABILITY THEORY AND RELATED FIELDS, 2017, 168 (3-4) : 557 - 600
[6] The problem of universality of nuclear mean-field parametrizations
Dubray, N
Dudek, J
Schunck, N
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS E-NUCLEAR PHYSICS, 2005, 14 (03) : 493 - 498
[7] Mean-Field Conditions for Percolation on Finite Graphs
Asaf Nachmias
[J]. Geometric and Functional Analysis, 2009, 19 : 1171 - 1194
[8] MEAN-FIELD CONDITIONS FOR PERCOLATION ON FINITE GRAPHS
Nachmias, Asaf
[J]. GEOMETRIC AND FUNCTIONAL ANALYSIS, 2009, 19 (04) : 1171 - 1194
[9] Cluster solver for dynamical mean-field theory with linear scaling in inverse temperature
Khatami, E.
Lee, C. R.
Bai, Z. J.
Scalettar, R. T.
Jarrell, M.
[J]. PHYSICAL REVIEW E, 2010, 81 (05):
[10] On the universality of distribution of ranked cluster masses at critical percolation
Sen, P
[J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (44): : 7673 - 7678

← 1 2 3 4 5 →