Growing spin model in deterministic and stochastic trees

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.

6 pages, 6 figures

References in corpus (19)

• Emergence of scaling in random networks
• Statistical mechanics of complex networks
• Novelty and Collective Attention
• Collective emotions online and their influence on community life
• Bayesian inference of epidemics on networks via Belief Propagation
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Negative emotions boost users activity at BBC Forum
• An Agent-Based Model of Collective Emotions in Online Communities
• Shortest paths and load scaling in scale-free trees
• Nonequilibrium phase transition due to social group isolation
• Structure and stability of online chat networks built on emotion-carrying links
• Attention Competition with Advertisement
• Entropy-growth-based model of emotionally charged online dialogues
• Analytical approach to model of scientific revolutions
• Exact solution of the Nonconsensus Opinion Model on the line
• Dynamics of interacting information waves in networks
• Dynamical phase transition due to preferential cluster growth of collective emotions in online communities
• Ferromagnetic Ising spin systems on the growing random tree
• Finite size induces crossover temperature in growing spin chains