Ferromagnetic Ising spin systems on the growing random tree

Abstract

We analyze the ferromagnetic Ising model on a scale-free tree; the growing random network model with the linear attachment kernel $A_k=k+\alpha$ introduced by [Krapivsky et al.: Phys. Rev. Lett. {\bf 85} (2000) 4629-4632]. 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 support the validity of this estimate.

15 pages, 5 figures

References in corpus (6)

• Critical phenomena in complex networks
• Inverted Berezinskii-Kosterlitz-Thouless Singularity and High-Temperature Algebraic Order in an Ising Model on a Scale-Free Hierarchical-Lattice Small-World Network
• Ising model on two connected Barabasi-Albert networks
• Distribution of Edge Load in Scale-free Trees
• Average distance in growing trees
• Dependence of the average to-node distance on the node degree for random graphs and growing networks

Cited by in corpus (4)

• Generating-function approach for bond percolations in hierarchical networks
• Critical Phase of Bond Percolations on Growing Networks
• Ising Model on a random network with annealed or quenched disorder
• Growing spin model in deterministic and stochastic trees