Finite size effects for the Ising model on random graphs with varying dilution

被引：7

作者：

Barre, Julien ^{[1
]}

Ciani, Antonia ^{[2
,3
,6
]}

Fanelli, Duccio ^{[4
,5
,6
]}

Bagnoli, Franco ^{[4
,5
,6
]}

Ruffo, Stefano ^{[4
,5
,6
]}

机构：

[1] Univ Nice Sophia Antipolis, CNRS, UMR 6621, Lab JA Dieudonne, F-06108 Nice, France

[2] Univ Florence, Dipartimento Fis, I-50019 Florence, Italy

[3] Ist Nazl Fis Nucl, I-50019 Florence, Italy

[4] Univ Florence, Dipartimento Energet, I-50139 Florence, Italy

[5] Ist Nazl Fis Nucl, I-50139 Florence, Italy

[6] Univ Florence, CSDC, Centro Interdipartimentale Studio Dinamiche Compl, I-50019 Florence, Italy

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2009年 / 388卷 / 17期

关键词：

Ising model; Random graphs; Finite size effects; Replica method; Cavity method;

D O I：

10.1016/j.physa.2009.04.024

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We investigate the finite size corrections to the equilibrium magnetization of an Ising model on a random graph with N nodes and N gamma edges, with 1 < gamma <= 2. By conveniently rescaling the coupling constant, the free energy is made extensive. As expected, the system displays a phase transition of the mean-field type for all the considered values of gamma at the transition temperature of the fully connected Curie-Weiss model. Finite size corrections are investigated for different values of the parameter gamma, using two different approaches: a replica based finite N expansion, and a cavity method. Numerical simulations are compared with theoretical predictions. The cavity based analysis is shown to agree better with numerics. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：3413 / 3425

页数：13

共 18 条

[11]

DEMBO A, 2008, ARXIV 08044726

[12] 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

[13] 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

[14]

Erdos P., 1959, Publ. Math. Debrecen, V6, P290, DOI DOI 10.5486/PMD.1959.6.3-4.12

[15]

Hartmann AK, 2005, PHASE TRANSITIONS IN COMBINATORIAL OPTIMIZATION PROBLEMS: BASICS, ALGORITHMS AND STATISTICAL MECHANICS, P1, DOI 10.1002/3527606734

[16] Ferromagnetic ordering in graphs with arbitrary degree distribution [J].

Leone, M ;

Vázquez, A ;

Vespignani, A ;

Zecchina, R .

EUROPEAN PHYSICAL JOURNAL B, 2002, 28 (02) :191-197

[17] EQUATION OF STATE CALCULATIONS BY FAST COMPUTING MACHINES [J].

METROPOLIS, N ;

ROSENBLUTH, AW ;

ROSENBLUTH, MN ;

TELLER, AH ;

TELLER, E .

JOURNAL OF CHEMICAL PHYSICS, 1953, 21 (06) :1087-1092

[18] The Bethe lattice spin glass revisited [J].

Mézard, M ;

Parisi, G .

EUROPEAN PHYSICAL JOURNAL B, 2001, 20 (02) :217-233

← 1 2 →