  We study the mixing time of systematic scan Glauber dynamics Ising model on
the complete graph. On the complete graph $K_n$, at each time, $k \leq n$
vertices are chosen uniformly random and are updated one by one according to
the uniformly randomly chosen permutations over the $k$ vertices. We show that
if $k = o(n^{1/3})$, the high temperature regime $\beta < 1$ exhibits cutoff
phenomena. For critical temperature regime $\beta = 1$, We prove that the
mixing time is of order $n^{3/2}k^{-1}$. For $\beta > 1$, we prove the mixing
time is of order $nk^{-1}\log n$ under the restricted dynamics.
