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In this paper, the Glauber dynamics for the Ising model on the completemultipartite graph $K_{np_1,\dots,np_m}$ is investigated where $0<p_i<1$ is theproportion of the vertices in the $i$th component. We show that the dynamicsexhibits the cutoff phenomena at $t_n = \frac{1}{2(1-\beta/\beta_{cr})} n\ln n$ with window size $O(n)$ in the high temperature regime $\beta< \beta_{cr}$where $\beta_{cr}$ is a constant only depending on $p_1,\dots,p_m$.Exponentially slow mixing is shown in the low temperature regime$\beta>\beta_{cr}$.

Cutoff phenomenon of the Glauber dynamics for the Ising model on complete multipartite graphs in the high temperature regime