The dynamics of the Blume-Emery-Griffiths model

The Fock-space method is presented to analyze the dynamics of the Blume-Emery-Griffiths (BEG) model including both spin-flip and spin-exchange processes with weighted transition rates. In this connection, the master equation on a lattice is formulated in a Quantum-Hamiltonian technique with second quantized operators. Introducing raising and lowering Para-Fermi operators for spin S = 1 the master equation is established for a three-state model where two states represent two different kinds of particles and the remaining state corresponds to an empty state. The coupled dynamical equations for the particle density and the local relative composition are derived including fluctuation corrections in lowest order of a gradient expansion. Although the underlying dynamics are subjected to the exclusion principle the resulting equations of motion may be classified according to the scheme due to Halperin and Hohenberg where the field-dependent kinetic coefficients are given explicitly. The homogeneous stationary solutions of these dynamical equations correspond to the mean-field approximation of the BEG Hamiltonian. For a special case, the diluted kinetic Ising model, phase separation is observed below a characteristic temperature. Furthermore, the crossover between thermal and non-thermal driven processes is discussed.