Clarification of the bootstrap percolation paradox

被引：27

作者：

De Gregorio, P ^{[1
]}

Lawlor, A ^{[1
]}

Bradley, P ^{[1
]}

Dawson, KA ^{[1
]}

机构：

[1] Natl Univ Ireland Univ Coll Dublin, Dept Chem, Irish Ctr Colloid Sci & Biomat, Dublin 4, Ireland

来源：

PHYSICAL REVIEW LETTERS | 2004年 / 93卷 / 02期

关键词：

D O I：

10.1103/PhysRevLett.93.025501

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the onset of the bootstrap percolation transition as a model of generalized dynamical arrest. Our results apply to two dimensions, but there is no significant barrier to extending them to higher dimensionality. We develop a new importance-sampling procedure in simulation, based on rare events around "holes", that enables us to access bootstrap lengths beyond those previously studied. By framing a new theory in terms of paths or processes that lead to emptying of the lattice we are able to develop systematic corrections to the existing theory and compare them to simulations. Thereby, for the first time in the literature, it is possible to obtain credible comparisons between theory and simulation in the accessible density range.

引用

页码：025501 / 1

页数：4

共 22 条

[11] Universality in lattice models of dynamic arrest: Introduction of an order parameter [J].

Lawlor, A ;

Reagan, D ;

McCullagh, GD ;

De Gregorio, P ;

Tartaglia, P ;

Dawson, KA .

PHYSICAL REVIEW LETTERS, 2002, 89 (24)

[12] Abelian cascade dynamics in bootstrap percolation [J].

Manna, SS .

PHYSICA A, 1998, 261 (3-4) :351-358

[13]

MARINARI E, CONDMAT0404214

[14] Bistability and hysteresis in tilted sandpiles [J].

Mehta, A ;

Barker, GC .

EUROPHYSICS LETTERS, 2001, 56 (05) :626-632

[15]

Polyakov A.M., 1987, CONT CONCEPTS PHYS, V3

[16] Hysteresis in the random-field Ising model and bootstrap percolation [J].

Sabhapandit, S ;

Dhar, D ;

Shukla, P .

PHYSICAL REVIEW LETTERS, 2002, 88 (19) :1972021-1972024

[17] ON THE BEHAVIOR OF SOME CELLULAR AUTOMATA RELATED TO BOOTSTRAP PERCOLATION [J].

SCHONMANN, RH .

ANNALS OF PROBABILITY, 1992, 20 (01) :174-193

[18]

STAUFFER D, COMMUNICATION

[19]

TONINELLI C, CONDMAT0306746

[20] ADDITION [J].

VANENTER, ACD .

JOURNAL OF STATISTICAL PHYSICS, 1991, 62 (1-2) :505-506

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