A numerical study of the 3D random interchange and random loop models

被引：10

作者：

Barp, Alessandro ^{[1
]}

Barp, Edoardo Gabriele ^{[1
]}

Briol, Francois-Xavier ^{[2
]}

Ueltschi, Daniel ^{[3
]}

机构：

[1] Univ Warwick, Dept Phys, Coventry CV4 7AL, W Midlands, England

[2] Univ Oxford, Dept Stat, Oxford OX1 3TG, England

[3] Univ Warwick, Dept Math, Coventry CV4 7AL, W Midlands, England

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2015年 / 48卷 / 34期

关键词：

random interchange model; random loop model; macroscopic loops; Poisson-Dirichlet distribution; QUANTUM;

D O I：

10.1088/1751-8113/48/34/345002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We have studied numerically the random interchange model and related loop models on the three-dimensional cubic lattice. We have determined the transition time for the occurrence of long loops. The joint distribution of the lengths of long loops is Poisson-Dirichlet with parameter 1 or 1/2.

引用

页数：12

共 21 条

[1] GEOMETRIC ASPECTS OF QUANTUM SPIN STATES [J].

AIZENMAN, M ;

NACHTERGAELE, B .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1994, 164 (01) :17-63

[2]

Alon G, 2010, DUKE MATH J IN PRESS

[3]

Angel O., 2003, DISCRETE MATH THEOR, P9

[4]

[Anonymous], COMMUNICATION

[5]

Berestycki N, 2012, B SOC MATH IN PRESS

[6] Emergence of giant cycles and slowdown transition in random transpositions and k-cycles [J].

Berestycki, Nathanael .

ELECTRONIC JOURNAL OF PROBABILITY, 2010, 16 :152-173

[7] Spatial random permutations and Poisson-Dirichlet law of cycle lengths [J].

Betz, Volker ;

Ueltschi, Daniel .

ELECTRONIC JOURNAL OF PROBABILITY, 2011, 16 :1173-1192

[8]

Friedli S, EQUILIBRIUM ST UNPUB

[9]

Goldschmidt C, 2011, CONTEMP MATH, V552, P177

[10] Lattice Permutations and Poisson-Dirichlet Distribution of Cycle Lengths [J].

Grosskinsky, Stefan ;

Lovisolo, Alexander A. ;

Ueltschi, Daniel .

JOURNAL OF STATISTICAL PHYSICS, 2012, 146 (06) :1105-1121

← 1 2 3 →