Ferromagnetic Ising spin systems on the growing random tree.
We analyze the ferromagnetic Ising model on a scale-free tree; the growing random tree model with the linear attachment kernel A(k) = k + alpha . We derive an estimate of the divergent temperature T(s) below which the zero-field susceptibility of the system diverges. Our result shows that T(s) is related to alpha as tanh(J/T(s)) = alpha/[2(alpha+1)] , where J is the ferromagnetic interaction. An analysis of exactly solvable limit for the model and numerical calculation supports the validity of this estimate.
Department of Physics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan. hase@statphys.sci.hokudai.ac.jp
Takehisa
T
Hasegawa
Koji
K
Nemoto