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Related Concept Videos

Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...
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Critical fluctuations in spatial complex networks.

Serena Bradde1, Fabio Caccioli, Luca Dall'Asta

  • 1International School for Advanced Studies, via Beirut 2/4, 34014, Trieste, Italy.

Physical Review Letters
|September 28, 2010
PubMed
Summary
This summary is machine-generated.

Critical fluctuations in the Ising model deviate from mean-field theory on spatial networks. Embedding complex networks in geometry reveals spectral properties that alter critical behavior, generalizing the Ginsburg criterion.

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Area of Science:

  • Statistical physics
  • Network science
  • Complex systems

Background:

  • The Ising model on complex networks typically exhibits mean-field behavior.
  • Anomalous mean-field solutions describe nontrivial phase diagrams in annealed complex networks.
  • Critical fluctuations in random complex networks usually adhere to mean-field predictions.

Purpose of the Study:

  • To investigate the breakdown of mean-field theory for critical fluctuations in complex networks.
  • To explore the impact of embedding networks in geometrical spaces on Ising model behavior.
  • To identify network properties governing critical fluctuations and generalize theoretical criteria.

Main Methods:

  • Analysis of the Ising model on annealed spatial networks.
  • Investigation of network spectral properties.
  • Generalization of the Ginsburg criterion for complex topologies.

Main Results:

  • Demonstration of a breakdown of mean-field critical fluctuations when networks are embedded in geometrical spaces.
  • Identification of specific spectral properties of networks that influence critical fluctuations.
  • Extension of the Ginsburg criterion to account for complex network structures.

Conclusions:

  • Embedding complex networks in geometrical spaces fundamentally alters critical fluctuation behavior.
  • Network spectral properties are key determinants of deviations from mean-field theory.
  • The generalized Ginsburg criterion provides a new framework for understanding criticality in complex spatial networks.