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We investigated the random-field Blume-Capel model, observing double hysteresis loops and return point memory in its magnetization. Simulations on random regular graphs align well with Bethe lattice calculations for negative external fields.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • The random-field Blume-Capel model is a key system for studying magnetic phase transitions.
  • Understanding its behavior under external fields and on complex networks is crucial.

Purpose of the Study:

  • To investigate the zero-temperature steady-state of the random-field Blume-Capel model with Glauber dynamics on random regular graphs.
  • To analyze magnetization behavior, including hysteresis, as a function of external magnetic fields.
  • To compare simulation results with theoretical calculations on a Bethe lattice.

Main Methods:

  • Simulations of the random-field Blume-Capel model on random regular graphs using spin-flip Glauber dynamics.
  • Analytical solution of the model on a Bethe lattice under the abelian dynamics approximation.
  • Comparison of simulation and theoretical results.

Main Results:

  • Observed double hysteresis loops in magnetization (m) versus external field (H).
  • Identified return point memory effects in the magnetization.
  • Found good agreement between random regular graph simulations and Bethe lattice calculations for negative external fields.

Conclusions:

  • The random-field Blume-Capel model exhibits complex magnetic behavior, including double hysteresis and memory effects.
  • Bethe lattice calculations provide a reliable approximation for the model's behavior on random regular graphs, particularly for negative fields.