  We study the equilibrium and dynamical properties of the ANNNI (axial
next-nearest-neighbor Ising) chain at the multiphase point. An interesting
property of the system is the macroscopic degeneracy of the ground state
leading to finite zero-temperature entropy. In our equilibrium study we
consider the effect of softening the spins. We show that the degeneracy of the
ground state is lifted and there is a qualitative change in the low temperature
behaviour of the system with a well defined low temperature peak of the
specific heat that carries the thermodynamic ``weight'' of the ground state
entropy. In our study of the dynamical properties, the stochastic Kawasaki
dynamics is considered. The Fokker-Planck operator for the process corresponds
to a quantum spin Hamiltonian similar to the Heisenberg ferromagnet but with
constraints on allowed states. This leads to a number of differences in its
properties which are obtained through exact numerical diagonalization,
simulations and by obtaining various analytic bounds.
