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This study investigates kinetic Ising models with self-interaction using Monte Carlo simulations. It reveals how different updating rules (sequential vs. parallel) affect equilibrium properties and critical dynamics, particularly in the presence of self-interaction.

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Area of Science:

  • Statistical physics
  • Complex systems

Background:

  • Kinetic Ising models are fundamental for understanding phase transitions and dynamics in magnetic systems.
  • Self-interaction and different updating rules (sequential, parallel) introduce complexities not fully captured by standard models.

Purpose of the Study:

  • To analyze the equilibrium phase diagrams and critical dynamics of kinetic Ising models with nearest-neighbor and self-interactions.
  • To compare the effects of random sequential updating versus parallel updating on model behavior.
  • To investigate the influence of weak and strong self-interaction limits on system properties.

Main Methods:

  • Monte Carlo simulations were employed to explore the phase diagrams and dynamics.
  • Analytic approximations were used to complement simulation results.
  • The study analyzed the Hamiltonians governing equilibrium properties under different updating schemes.

Main Results:

  • Equilibrium Hamiltonians differ for sequential and parallel updating, both featuring multispin and non-nearest-neighbor couplings.
  • For parallel updating, weak self-interaction leads to decoupled sublattices and checkerboard patterns, causing singular critical lines.
  • In the strong self-interaction limit, both updating methods yield equilibrium properties described by a nearest-neighbor Hamiltonian with doubled interaction strength.

Conclusions:

  • The updating mechanism significantly impacts the equilibrium phase diagrams and critical dynamics of kinetic Ising models with self-interaction.
  • Self-interaction introduces non-trivial couplings and can lead to emergent patterns and altered critical behavior.
  • The study provides insights into the complex interplay between dynamics, interactions, and emergent properties in statistical physics models.