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Small-world hypergraphs on a bond-disordered Bethe lattice.

D Bollé1, R Heylen

  • 1Katholieke Universiteit Leuven, Instituut voor Theoretische Fysica, Celestijnenlaan 200D, B-3001 Leuven, Belgium.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary
This summary is machine-generated.

This study investigates spin systems with disorder on complex hypergraphs. Researchers analyzed thermodynamic properties and transitions, finding results consistent with simulations.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • Spin systems are fundamental models in statistical mechanics.
  • Disorder and complex network structures significantly impact system properties.
  • Small-world networks and hypergraphs offer realistic models for complex systems.

Purpose of the Study:

  • To investigate the thermodynamic properties of spin systems with bond-disorder.
  • To analyze the behavior of these systems on small-world hypergraphs.
  • To understand the influence of disorder on ferromagnetic and spin-glass transitions.

Main Methods:

  • Superimposing a one-dimensional Ising chain onto a random Bethe graph.
  • Employing transfer-matrix techniques.
  • Deriving fixed-point equations in replica symmetric and one-step replica symmetry breaking approximations.

Main Results:

  • Determined static and dynamic ferromagnetic transitions and spin-glass transitions.
  • Identified fixed-point equations for order parameters and free energy.
  • Quantified corrections to transitions upon incorporating one-step replica symmetry breaking.

Conclusions:

  • The theoretical framework accurately describes thermodynamic properties and transitions.
  • Results align with experimental observations from Monte Carlo simulations.
  • The study provides insights into disordered spin systems on complex network topologies.