Ferromagnetic ordering in graphs with arbitrary degree distribution
By M. Leone, A. Vázquez, Alessandro Vespignani, Riccardo Zecchina. 2002
176 citations recorded by the source corpus.
Abstract:We present a detailed study of the phase diagram of the Ising model in random graphs with arbitrary degree distribution. By using the replica method we compute exactly the value of the critical temperature and the associated critical exponents as a function of the moments of the degree distribution. Two regimes of the degree distribution are of particular interest. In the case of a divergent second moment, the system is ferromagnetic at all temperatures. In the case of a finite second moment and a divergent fourth moment, there is a ferromagnetic transition characterized by non-trivial critical exponents. Finally, if the fourth moment is finite we recover the mean field exponents. These results are analyzed in detail for power-law distributed random graphs.
Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/001ec6366dfb70cd6d4670a3d977974114fcd13b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Condensed Matter Physics
- Mark Newman
- José Fernando Ferreira Mendes
- Sergey N. Dorogovtsev
- Alexander V. Goltsev
- Santo Fortunato
- Claudio Castellano
In Statistical and Nonlinear Physics
- Mark Newman
- Santo Fortunato
- Francisco Aparecido Rodrigues
- Claudio Castellano
- Alexander V. Goltsev
- Sergey N. Dorogovtsev
- José Fernando Ferreira Mendes
- Luciano da Fontoura Costa
Citations in the corpus
- Statistical physics of social dynamics (2007, background): “This is similar to what occurs for the Ising model on scale-free networks, where the transition temperature diverges with system size (Leone et al., 2002).”
- Analyzing and modeling real-world phenomena with complex networks: a survey of applications (2007, methodology): “The analytical solution for this model in a network with arbitrary degree di stribution was found in [455, 456].”
- Critical phenomena in complex networks (2007, methodology): “Dorogovtsev et al. (2005) found that in these networks the pair correlation function 〈SiSj〉 between the second and more distant neighbors vanishes in the limit N → ∞.”
- Binary-state dynamics on complex networks: pair approximation and beyond (2012, unknown): “[25,26] for the critical behavior on scale-free networks can also be applied here and gives results described in Sec.”
- The Structure and Function of Complex Networks (2003, background): “191, 202, 256, 337, 429, and the model has also been studied on random graphs [112, 264] and on net-”