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Mixed-spin ising model with one- and two-spin competing dynamics

Godoy1, Figueiredo

  • 1Departamento de Fisica, Universidade Federal de Santa Catarina, 88040-900 Florianopolis, SC, Brazil.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
Summary

This study investigates a kinetic Ising model with two spin types, revealing phase transitions between ferrimagnetic, paramagnetic, and antiferrimagnetic states. The research explores system dynamics using competing transition rates and a dynamical pair approximation.

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Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Complex Systems

Background:

  • The kinetic Ising model is a fundamental framework for understanding magnetic phenomena and phase transitions.
  • Investigating systems with competing dynamics and multiple spin types is crucial for modeling complex materials.
  • Previous studies often focus on single spin types or simpler transition mechanisms.

Purpose of the Study:

  • To determine the stationary states of a kinetic Ising model incorporating two distinct spin types (sigma=1/2 and S=1).
  • To analyze the system's time evolution and phase diagram under competing relaxation and energy input processes.
  • To map the transitions between ferrimagnetic, paramagnetic, and antiferrimagnetic phases.

Main Methods:

  • Utilized a kinetic Ising model with two interpenetrating sublattices for sigma=1/2 and S=1 spins.

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  • Employed competing transition rates: Glauber process (one-spin flips) and simultaneous pair flips (energy input).
  • Applied the dynamical pair approximation to derive equations of motion for sublattice magnetizations and correlations.

    • Main Results:

    • Derived the time evolution for system state probabilities.
    • Obtained equations of motion for sublattice magnetizations and nearest-neighbor correlation functions.
    • Constructed the phase diagram for stationary states, identifying two continuous transition lines.

    Conclusions:

    • The kinetic Ising model with two spin types exhibits rich phase behavior.
    • Continuous transitions were observed between paramagnetic and ferrimagnetic phases, and between paramagnetic and antiferrimagnetic phases.
    • The dynamical pair approximation provides a viable method for analyzing such complex magnetic systems.