Julia sets and complex singularities in diamond-like hierarchical Potts models

被引：21

作者：

Qiao, JY ^{[1
]}

机构：

[1] China Univ Min & Technol, Ctr Math, Beijing 100083, Peoples R China

来源：

SCIENCE IN CHINA SERIES A-MATHEMATICS | 2005年 / 48卷 / 03期

关键词：

Julia set; phase transition; iteration; rational mapping;

D O I：

10.1360/04ys0180

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the phase transition of the Potts model on diamond-like hierarchical lattices. It is shown that the set of the complex singularities is the Julia set of a rational mapping. An interesting problem is how are these singularities continued to the complex plane. In this paper, by the method of complex dynamics, we give a complete description about the connectivity of the set of the complex singularities.

引用

页码：388 / 412

页数：25

共 26 条

[1] Julia sets and complex singularities in diamond-like hierarchical Potts models
Jianyong Qiao
Science in China Series A: Mathematics, 2005, 48 : 388 - 412
[2] Julia sets and complex singularities in diamond-like hierarchical Potts models
QIAO Jianyong Center of Mathematics China University of Mining Technology Beijing China
ScienceinChina,SerA., 2005, Ser.A.2005 (03) : 388 - 412
[3] Julia sets and complex singularities in diamond-like hierarchical Potts models
QIAO Jianyong Center of Mathematics
Science China Mathematics, 2005, (03) : 388 - 412
[4] Consensus of Julia Sets of Potts Models on Diamond-Like Hierarchical Lattice
Lu, Xiaoling
Sun, Weihua
IEEE ACCESS, 2022, 10 : 128670 - 128681
[5] JULIA SETS AND COMPLEX SINGULARITIES IN HIERARCHICAL ISING-MODELS
BLEHER, PM
LYUBICH, MY
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[6] Jordan domain and Fatou set concerning diamond-like hierarchical Potts models
Qiao Jianyong
Gao Junyang
NONLINEARITY, 2007, 20 (01) : 119 - 131
[7] Fractal Dynamics and Control of the Fractional Potts Model on Diamond-Like Hierarchical Lattices
Sun, Weihua
Liu, Shutang
DISCRETE DYNAMICS IN NATURE AND SOCIETY, 2020, 2020
[8] Julia Sets and Complex Singularities of Free Energies
不详
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 234 (1102) : 1 - +
[9] Complex-temperature singularities in Potts models on the square lattice
Matveev, Victor
Shrock, Robert
Physical Review E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1996, 54 (06):
[10] Complex-temperature singularities in Potts models on the square lattice
Matveev, V
Shrock, R
PHYSICAL REVIEW E, 1996, 54 (06): : 6174 - 6185

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