  We construct strong stationary dual chains for Ising model on a circle,
non-symmetric random walk on square lattice and a random walk on hypercube. The
strong stationary dual chains are all sharp and have the same state space as
original chains. We use M\"obius monotonicity of these chains with respect to
natural orderings of the corresponding state spaces. This method provides an
easy way to find eigenvalues in the Ising model and for a random walk on
hypercube.
  Keywords: Markov chains; stochastic monotonicity; eigenvalues; M\"obius
monotonicity; strong stationary duality; strong stationary times; separation
distance; mixing time; Ising model; hypercube
