  We study the multi-component Ising model, which is also known as the block
Ising model. In this model, the particles are partitioned into a fixed number
of groups with a fixed proportion, and the interaction strength is determined
by the group to which each particle belongs. We demonstrate that the Glauber
dynamics on our model exhibits the cutoff$\mbox{--}$metastability phase
transition as passing the critical inverse-temperature $\beta_{cr}$, which is
determined by the proportion of the groups and their interaction strengths,
regardless of the total number of particles. For $\beta<\beta_{cr}$, the
dynamics shows a cutoff at $\alpha n\log n$ with a window size $O(n)$, where
$\alpha$ is a constant independent of $n$. For $\beta=\beta_{cr}$, we prove
that the mixing time is of order $n^{3/2}$. In particular, we deduce the
so-called non-central limit theorem for the block magnetizations to validate
the optimal bound at $\beta=\beta_{cr}$. For $\beta>\beta_{cr}$, we examine the
metastability, which refers to the exponential mixing time. Our results, based
on the position of the employed Ising model on the complete multipartite graph,
generalize the results of previous versions of the model.
