Incipient Infinite Cluster in 2D Ising Percolation

被引：0

作者：

Higuchi, Y. ^{[1
]}

Kinoshita, K. ^{[1
]}

Takei, M. ^{[2
]}

Zhang, Y. ^{[3
]}

机构：

[1] Kobe Univ, Dept Math, Kobe, Hyogo 6578501, Japan

[2] Yokohama Natl Univ, Fac Engn, Dept Appl Math, Yokohama, Kanagawa 2408501, Japan

[3] Univ Colorado, Dept Math, Colorado Springs, CO 80933 USA

来源：

MARKOV PROCESSES AND RELATED FIELDS | 2014年 / 20卷 / 02期

关键词：

percolation; Ising model; incipient infinite cluster; TRANSITION; SHARP;

D O I：

暂无

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider the percolation problem in the high-temperature Ising model on the two-dimensional square lattice at or near critical external fields. The incipient infinite cluster (IIC) measure in the sense of Kesten is constructed. As a consequence, we can obtain some geometric properties of TIC. The result holds also for the triangular lattice.

引用

收藏

页码：173 / 182

页数：10

相关论文

共 11 条

[1] THE PHASE-TRANSITION IN A GENERAL-CLASS OF ISING-TYPE MODELS IS SHARP [J].

AIZENMAN, M ;

BARSKY, DJ ;

FERNANDEZ, R .

JOURNAL OF STATISTICAL PHYSICS, 1987, 47 (3-4) :343-374

[2] The High Temperature Ising Model on the Triangular Lattice is a Critical Bernoulli Percolation Model [J].

Balint, Andras ;

Camia, Federico ;

Meester, Ronald .

JOURNAL OF STATISTICAL PHYSICS, 2010, 139 (01) :122-138

[3] CORRELATION INEQUALITIES ON SOME PARTIALLY ORDERED SETS [J].

FORTUIN, CM ;

KASTELEY.PW ;

GINIBRE, J .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1971, 22 (02) :89-&

[4] A SHARP TRANSITION FOR THE 2-DIMENSIONAL ISING PERCOLATION [J].

HIGUCHI, Y .

PROBABILITY THEORY AND RELATED FIELDS, 1993, 97 (04) :489-514

[5] COEXISTENCE OF INFINITE (ASTERISK)-CLUSTERS .2. ISING PERCOLATION IN 2 DIMENSIONS [J].

HIGUCHI, Y .

PROBABILITY THEORY AND RELATED FIELDS, 1993, 97 (1-2) :1-33

[6]

HIGUCHI Y., 2010, ARXIV10101586, V1010, P1586

[7] Scaling Relations for Two-Dimensional Ising Percolation [J].

Higuchi, Yasunari ;

Takei, Masato ;

Zhang, Yu .

JOURNAL OF STATISTICAL PHYSICS, 2012, 148 (05) :777-799

[8] THE INCIPIENT INFINITE CLUSTER IN TWO-DIMENSIONAL PERCOLATION [J].

KESTEN, H .

PROBABILITY THEORY AND RELATED FIELDS, 1986, 73 (03) :369-394

[9] UNIQUENESS OF EQUILIBRIUM STATE FOR ISING SPIN SYSTEMS [J].

LEBOWITZ, JL ;

MARTINLO.A .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1972, 25 (04) :276-&

[10] USE OF SMALL-EXTERNAL-FIELDS IN PROBLEM OF SYMMETRY BREAKDOWN IN STATISTICAL MECHANICS [J].

RUELLE, D .

ANNALS OF PHYSICS, 1972, 69 (02) :364-&