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Area of Science:

  • Statistical physics
  • Network science
  • Computational physics

Background:

  • The zero-temperature Ising model exhibits distinct behaviors in dense versus sparse random graphs.
  • In dense graphs, it reaches an ordered ground state, while sparse graphs lead to disordered dynamics near zero magnetization.

Purpose of the Study:

  • To investigate the nonequilibrium transition in the Ising model on random graphs.
  • To characterize the system's behavior, including bistability and absorption time, as a function of average degree and system size.

Main Methods:

  • Simulations of the zero-temperature Ising model on random graphs.
  • Analysis of magnetization dynamics and absorption times.
  • Investigation of the transition point and system bistability.

Main Results:

  • A nonequilibrium transition occurs at an average degree that scales with graph size.
  • The system exhibits bistability, with magnetization distributions peaking at zero and unity.
  • Average absorption time shows non-monotonic behavior with average degree and scales with system size.

Conclusions:

  • The study identifies a critical average degree for the transition in sparse random graphs.
  • Bistability and complex absorption time dynamics are key features of this nonequilibrium transition.
  • Findings are relevant for understanding community detection, opinion dynamics, and games on networks.