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Julian Sienkiewicz1

  • 1Faculty of Physics, Center of Excellence for Complex Systems Research, Warsaw University of Technology, Koszykowa 75, PL-00-662 Warsaw, Poland.

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Summary
This summary is machine-generated.

We analyzed the asymmetric Ising model on scale-free trees. The crossover temperature for maximal magnetization shows non-monotonous behavior and decays logarithmically with the number of nodes.

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Area of Science:

  • Statistical physics
  • Complex networks
  • Phase transitions

Background:

  • The asymmetric Ising model is a fundamental model in statistical mechanics used to study magnetic phenomena.
  • Scale-free networks exhibit unique topological properties influencing system dynamics.
  • Understanding phase transitions in network models is crucial for various scientific domains.

Purpose of the Study:

  • To investigate the behavior of the asymmetric Ising model on deterministic and stochastic scale-free trees.
  • To predict the non-monotonous behavior of magnetization under external fields.
  • To analyze the scaling of crossover temperature with network size.

Main Methods:

  • Analytical solution of the asymmetric Ising model.
  • Implementation on deterministic and stochastic scale-free tree topologies.
  • Analysis of magnetization and crossover temperature as a function of external field and network size.

Main Results:

  • The asymmetric Ising model exhibits non-monotonous behavior for external fields smaller than the coupling constant J.
  • A crossover temperature associated with maximal magnetization was identified.
  • This crossover temperature decays approximately as (lnlnN)^(-1) with the number of nodes N in both deterministic and stochastic scale-free trees.

Conclusions:

  • The study provides a theoretical framework for understanding magnetic phase transitions in complex network structures.
  • The findings highlight the significant impact of network topology on the behavior of the Ising model.
  • The predicted scaling law offers insights into the collective behavior of systems on large-scale networks.