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Updated: Jun 21, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

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Published on: September 8, 2023

Coupled order-parameter system on a scale-free network.

V Palchykov1, C von Ferber, R Folk

  • 1Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, UA-79011 Lviv, Ukraine. palchykov@icmp.lviv.ua

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 8, 2009
PubMed
Summary
This summary is machine-generated.

This study analyzes two scalar order parameters on scale-free networks, revealing two ordering types. Critical exponents match single-parameter models, but amplitude ratios and susceptibilities show unique behavior, including divergent transverse susceptibility.

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Last Updated: Jun 21, 2026

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
05:30

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

  • Statistical physics
  • Complex networks
  • Condensed matter theory

Background:

  • Landau theory provides a phenomenological framework for phase transitions.
  • Scale-free networks exhibit unique topological properties influencing system behavior.
  • Understanding systems with multiple order parameters is crucial for complex phenomena.

Purpose of the Study:

  • To analyze a system with two scalar order parameters on a complex scale-free network.
  • To investigate the interplay between phenomenological Landau theory and microscopic spin Hamiltonians.
  • To characterize the ordering behavior and critical properties of this two-parameter system.

Main Methods:

  • Analysis in the spirit of Landau theory.
  • Study of a specific spin Hamiltonian using the mean-field approximation.
  • Investigation of critical exponents, amplitude ratios, and susceptibilities.

Main Results:

  • Two distinct ordering scenarios identified: one parameter zero, or both non-zero and equal.
  • Critical exponents are consistent with single order parameter models on scale-free networks.
  • Notable differences observed in amplitude ratios and susceptibilities, including divergent transverse susceptibility at T

Conclusions:

  • The two-scalar order parameter system on scale-free networks exhibits unique characteristics distinct from single-parameter models.
  • The presence of Goldstone modes is linked to the divergent transverse susceptibility.
  • This research offers insights into the complex ordering behaviors in network systems.