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Higher-order Ising model on hypergraphs.

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Higher-order interactions in Ising models influence collective behavior. Introducing interactions beyond three-body terms shifts phase transitions from continuous to abrupt, impacting complex systems research.

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Area of Science:

  • Statistical Physics
  • Complex Systems

Background:

  • Collective behavior in networked systems is influenced by non-dyadic, higher-order interactions.
  • Understanding these interactions is crucial for modeling complex phenomena.

Purpose of the Study:

  • To investigate a novel Ising model incorporating higher-order interactions.
  • To characterize the phase transitions between ordered and disordered states in this model.

Main Methods:

  • Mean-field treatment to analyze phase transitions.
  • Georges-Yedidia expansion to refine approximations beyond mean-field.
  • Comparison with traditional p-spin models.

Main Results:

  • Mean-field analysis shows continuous transitions with three-body interactions, becoming abrupt with higher orders.
  • Beyond mean-field, a quantitative shift in the critical point was observed without altering the universality class.
  • The study highlights differences from traditional p-spin models.

Conclusions:

  • Higher-order interactions significantly alter phase transition dynamics in Ising models.
  • Investigating systems beyond three-body interactions reveals new collective phenomena.
  • The findings underscore the importance of higher-order interactions in complex systems.