We derive an exact expression for the magnetization and the zero-field susceptibility of the Ising model on a random graph with degree distribution P (k) ∝ k-γ and with a boundary consisting of leaves, that is, vertices whose degree is 1. The system has no magnetization at any finite temperature, and the susceptibility diverges below a certain temperature Ts depending on the exponent γ. In particular, Ts reaches infinity for γ≤4. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks.
|Journal||Physical Review E - Statistical, Nonlinear, and Soft Matter Physics|
|Publication status||Published - 2007 Feb 21|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics