Growing spin model in deterministic and stochastic trees

TL;DR

This paper analyzes the growing spin model on deterministic and stochastic trees, revealing non-monotonous behavior and a specific decay pattern of the crossover temperature as the network size increases.

Contribution

It provides the first analytical solution of the growing asymmetric Ising model on these tree topologies, highlighting its complex behavior and scaling properties.

Findings

Non-monotonous behavior for external fields smaller than J

Crossover temperature decays as (ln ln N)^{-1}

Predicts behavior for large network sizes

Abstract

We solve the growing asymmetric Ising model [Phys. Rev. E 89, 012105 (2014)] in the topologies of deterministic and stochastic (random) scale-free trees predicting its non-monotonous behavior for external fields smaller than the coupling constant $J$. In both cases we indicate that the crossover temperature corresponding to maximal magnetization decays approximately as $(\ln \ln N)^{-1}$, where $N$ is the number of nodes in the tree.