Critical relaxation of the one-dimensional Blume-Emery-Griffiths model

A model for the critical relaxation in the one-dimensional Ising-type S=1 spin system is presented. This model is equivalent to the Blume-Emery-Griffiths model and exhibits two simple critical points and one tricritical point. The kinetic behavior is studied using the real-space renormalization-group approach. In the two critical points we find that the critical slowing down is described by the dynamic exponent z, z=2. In each point this exponent belongs to the critical order parameter, while the second order parameter relaxes faster, with z=1 or 0. At the critical point the two order parameters relax with the same z, z=1.