Graphical representations for Ising systems in external fields

被引：24

作者：

Chayes, L ^{[1
]}

Machta, J

Redner, O

机构：

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

[2] Univ Massachusetts, Dept Phys & Astron, Amherst, MA 01003 USA

[3] Univ Tubingen, Inst Theoret Phys, D-72076 Tubingen, Germany

来源：

JOURNAL OF STATISTICAL PHYSICS | 1998年 / 93卷 / 1-2期

关键词：

cluster methods; external fields; RFIM;

D O I：

10.1023/B:JOSS.0000026726.43558.80

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

A graphical representation based on duplication is developed that is suitable for the study of Ising systems in external fields. Two independent replicas of the Ising system in the same field are treated as a single four-state (Ashkin-Teller) model. Bonds in the graphical representation connect the Ashkin-Teller spins. For ferromagnetic systems it is proved that ordering is characterized by percolation in this representation. The representation leads immediately to cluster algorithms; some applications along these lines are discussed.

引用

页码：17 / 32

页数：16

共 16 条

[1] DISCONTINUITY OF THE MAGNETIZATION IN ONE-DIMENSIONAL 1/[X-Y]2 ISING AND POTTS MODELS [J].

AIZENMAN, M ;

CHAYES, JT ;

CHAYES, L ;

NEWMAN, CM .

JOURNAL OF STATISTICAL PHYSICS, 1988, 50 (1-2) :1-40

[2] Graphical representations and cluster algorithms II [J].

Chayes, L ;

Machta, J .

PHYSICA A, 1998, 254 (3-4) :477-516

[3] Graphical representations and cluster algorithms .1. Discrete spin systems [J].

Chayes, L ;

Machta, J .

PHYSICA A, 1997, 239 (04) :542-601

[4] CLUSTERS AND ISING CRITICAL DROPLETS - A RENORMALIZATION GROUP-APPROACH [J].

CONIGLIO, A ;

KLEIN, W .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1980, 13 (08) :2775-2780

[5] GENERALIZATION OF THE FORTUIN-KASTELEYN-SWENDSEN-WANG REPRESENTATION AND MONTE-CARLO ALGORITHM [J].

EDWARDS, RG ;

SOKAL, AD .

PHYSICAL REVIEW D, 1988, 38 (06) :2009-2012

[6] RANDOM-CLUSTER MODEL .1. INTRODUCTION AND RELATION TO OTHER MODELS [J].

FORTUIN, CM ;

KASTELEYN, PW .

PHYSICA, 1972, 57 (04) :536-+

[7]

Georgii H.-O., 1988, Gibbs Measures and Phase Transitions

[8] Geometric cluster Monte Carlo simulation [J].

Heringa, JR ;

Blote, HWJ .

PHYSICAL REVIEW E, 1998, 57 (05) :4976-4978

[9] The simple-cubic lattice gas with nearest-neighbour exclusion: Ising universality [J].

Heringa, JR ;

Blote, HWJ .

PHYSICA A, 1996, 232 (1-2) :369-374

[10]

HERINGA JR, 1988, CLUSTER DYNAMICS UNI

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