Ising model on the scale-free network with a Cayley-tree-like structure.
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) proportional, k-gamma 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 gamma. In particular, Ts reaches infinity for gamma<or=4. These results are completely different from those of the case having no boundary, indicating the nontrivial roles of the leaves in the networks.
Hasegawa
Takehisa
T
Division of Physics, Hokkaido University, Sapporo, Japan. hase@statphys.sci.hokudai.ac.jp
Nemoto
Koji
K