  Hamiltonians for general multi-state spin-glass systems with Ising symmetry
are derived for both sequential and synchronous updating of the spins. The
possibly different behaviour caused by the way of updating is studied in detail
for the (anti)-ferromagnetic version of the models, which can be solved
analytically without any approximation, both thermodynamically via a
free-energy calculation and dynamically using the generating functional
approach. Phase diagrams are discussed and the appearance of two-cycles in the
case of synchronous updating is examined. A comparative study is made for the
Q-Ising and the Blume-Emery-Griffiths ferromagnets and some interesting
physical differences are found. Numerical simulations confirm the results
obtained.
