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This study explores phase transitions in a Heisenberg model using Monte Carlo simulations. It reveals second-order and first-order phase transitions, alongside unstable self-organization leading to ferromagnetic phases.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Computational Physics

Background:

  • Investigates the isotropic Heisenberg model on a simple cubic lattice.
  • Examines systems driven by competing Glauber and Kawasaki dynamics.

Purpose of the Study:

  • To analyze the phase diagram of temperature (T) versus Glauber dynamics probability (q).
  • To understand the interplay between thermal fluctuations and external energy flux.
  • To identify phase transitions and self-organization phenomena.

Main Methods:

  • Employs Monte Carlo simulations.
  • Models system evolution under Glauber dynamics (thermal reservoir) and Kawasaki dynamics (external flux).
  • Analyzes the phase diagram (T vs. q).

Main Results:

  • Identifies second-order phase transitions at high q and intermediate T.
  • Observes first-order phase transitions below a tricritical point (q_t=0.615, T_t=0.905).
  • Demonstrates unstable self-organization: antiferromagnetic phase only at q=0, evolving to ferromagnetic phase as q increases at low T.

Conclusions:

  • The competition between Glauber and Kawasaki dynamics dictates system behavior.
  • Phase transitions are sensitive to temperature and the balance of dynamics.
  • The system exhibits non-equilibrium self-organization, favoring ferromagnetic order under specific conditions.