# Ising model on the Apollonian network with node dependent interactions - Condensed Matter > Statistical Mechanics

Ising model on the Apollonian network with node dependent interactions - Condensed Matter > Statistical Mechanics - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

Abstract: This work considers an Ising model on the Apollonian network, where theexchange constant $J {i,j}\sim1-k ik j^\mu$ between two neighboring spins$i,j$ is a function of the degree $k$ of both spins. Using the exactgeometrical construction rule for the network, the thermodynamical and magneticproperties are evaluated by iterating a system of discrete maps that allows forvery precise results in the thermodynamic limit. The results can be compared tothe predictions of a general framework for spins models on scale-free networks,where the node distribution $Pk\sim k^{-\gamma}$, with node dependentinteracting constants. We observe that, by increasing $\mu$, the criticalbehavior of the model changes, from a phase transition at $T=\infty$ for auniform system $\mu=0$, to a T=0 phase transition when $\mu=1$: in thethermodynamic limit, the system shows no exactly critical behavior at a finitetemperature. The magnetization and magnetic susceptibility are found to presentnon-critical scaling properties.

Autor: R. F. S. Andrade, J. S. Andrade Jr., H. J. Herrmann

Fuente: https://arxiv.org/