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Generalized mean-field theory for Ising spins in small world networks
Phys. Rev. E 71, 046111 – Published 12 April, 2005
DOI: https://doi.org/10.1103/PhysRevE.71.046111
Abstract
A generalization of mean-field theory for random systems is described. The results of that analytic model could be reconciled with the results of numerical calculations of the Curie temperature for a system of Ising spins in small world (SW) networks by introducing the effective interaction energy associated with long-range links which exceeds the real energy of spin interaction. Such a model describes qualitatively well the increasing Curie temperature with the growth of the long-range links fraction in the two-dimensional SW system with fixed coordination number. On the basis of simple physical considerations, concentration dependences are found for SW systems of different dimensions.
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References (17)
- R. Albert and A-L. Barabási, Rev. Mod. Phys. 74, 47 (2002).
- D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998).
- M. Gitterman, J. Phys. A 33, 8373 (2000).
- A. Barrat and M. Weigt, Eur. Phys. J. B 13, 547 (2000).
- B. J. Kim, H. Hong, P. Holme, G. S. Jeon, P. Minnhagen, and M. Y. Choi, Phys. Rev. E 64, 056135 (2001).
- C. P. Herrero, Phys. Rev. E 65, 066110 (2002).
- H. Hong, B. J. Kim, and M. Y. Choi, Phys. Rev. E 66, 018101 (2002).
- M. A. Novotny and S. M. Wheeler, Braz. J. Phys. 34, 395 (2004).
- R. Baxter, Exactly Solved Models in Statistical mechanics (Academic Press, London, New York, 1982).
- T. Hill, Statistical Mechanics (McGraw-Hill, New York, 1956).
- M. W. Klein and R. Brout, Phys. Rev. 132, 2412 (1963).
- M. Thomsen, M. F. Thorpe, T. C. Choy, and D. Sherrington, Phys. Rev. B 30, 250 (1984); T. C. Choy, D. Sherrington, M. Thomsen, and M. F. Thorpe, ibid. 31, 7355 (1985); M. Thomsen, M. F. Thorpe, T. C. Choy, D. Sherrington, and H. J. Sommers, ibid. 33, 1931 (1986).
- B. E. Vugmeister and M. D. Glinchuk, Rev. Mod. Phys. 62, 993 (1990).
- A. P. Young, J. D. Reger, and K. Binder, in Monte-Carlo Methods in Statistical Mechanics, edited by K. Binder (Springer, Berlin, 1992).
- V. S. Dotsenko, Phys. Usp. 38, 457 (1995).
- Tian-Yi Cai and Zhen-Ya Li, Int. J. Mod. Phys. B 18, 2575 (2004).
- R. B. Griffiths, Phys. Rev. 136, A437 (1964).