Ising model on the Apollonian network with node-dependent interactions

被引:30
作者
Andrade, R. F. S. [1 ,2 ]
Andrade, J. S., Jr. [2 ,3 ]
Herrmann, H. J. [2 ,3 ]
机构
[1] Univ Fed Bahia, Inst Fis, BR-40210210 Salvador, BA, Brazil
[2] ETH Honggerberg, IfB, CH-8093 Zurich, Switzerland
[3] Univ Fed Ceara, Dept Fis, BR-60455760 Fortaleza, Ceara, Brazil
来源
PHYSICAL REVIEW E | 2009年 / 79卷 / 03期
关键词
complex networks; Ising model; magnetic susceptibility; magnetic transitions; magnetisation; thermodynamic properties; COMPLEX NETWORKS;
D O I
10.1103/PhysRevE.79.036105
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
This work considers an Ising model on the Apollonian network, where the exchange constant J(i,j)similar to 1/(k(i)k(j))(mu) between two neighboring spins (i,j) is a function of the degree k of both spins. Using the exact geometrical construction rule for the network, the thermodynamical and magnetic properties are evaluated by iterating a system of discrete maps that allows for very precise results in the thermodynamic limit. The results can be compared to the predictions of a general framework for spin models on scale-free networks, where the node distribution P(k)similar to k(-gamma), with node-dependent interacting constants. We observe that, by increasing mu, the critical behavior of the model changes from a phase transition at T=infinity for a uniform system (mu=0) to a T=0 phase transition when mu=1: in the thermodynamic limit, the system shows no true critical behavior at a finite temperature for the whole mu >= 0 interval. The magnetization and magnetic susceptibility are found to present noncritical scaling properties.
引用
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页数:7
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共 20 条
[1]   Ferromagnetic phase transition in Barabasi-Albert networks [J].
Aleksiejuk, A ;
Holyst, JA ;
Stauffer, D .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 310 (1-2) :260-266
[2]   Apollonian networks: Simultaneously scale-free, small world, Euclidean, space filling, and with matching graphs [J].
Andrade, JS ;
Herrmann, HJ ;
Andrade, RFS ;
da Silva, LR .
PHYSICAL REVIEW LETTERS, 2005, 94 (01)
[3]   Magnetic models on Apollonian networks [J].
Andrade, RFS ;
Herrmann, HJ .
PHYSICAL REVIEW E, 2005, 71 (05)
[4]   Detailed characterization of log-periodic oscillations for an aperiodic Ising model [J].
Andrade, RFS .
PHYSICAL REVIEW E, 2000, 61 (06) :7196-7199
[5]   Emergence of scaling in random networks [J].
Barabási, AL ;
Albert, R .
SCIENCE, 1999, 286 (5439) :509-512
[6]   Complex networks: Structure and dynamics [J].
Boccaletti, S. ;
Latora, V. ;
Moreno, Y. ;
Chavez, M. ;
Hwang, D. -U. .
PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS, 2006, 424 (4-5) :175-308
[7]   Characterization of complex networks: A survey of measurements [J].
Costa, L. Da F. ;
Rodrigues, F. A. ;
Travieso, G. ;
Boas, P. R. Villas .
ADVANCES IN PHYSICS, 2007, 56 (01) :167-242
[8]   What are the best concentric descriptors for complex networks? [J].
Costa, Luciano da Fontoura ;
Silva Andrade, Roberto Fernandes .
NEW JOURNAL OF PHYSICS, 2007, 9
[9]   Critical phenomena in complex networks [J].
Dorogovtsev, S. N. ;
Goltsev, A. V. ;
Mendes, J. F. F. .
REVIEWS OF MODERN PHYSICS, 2008, 80 (04) :1275-1335
[10]   Ising model on networks with an arbitrary distribution of connections [J].
Dorogovtsev, SN ;
Goltsev, AV ;
Mendes, JFF .
PHYSICAL REVIEW E, 2002, 66 (01) :1-016104