  The Peierls argument is a mathematically rigorous and intuitive method to
show the presence of a non-vanishing spontaneous magnetization in some lattice
models. This argument is typically explained for the $D=2$ Ising model in a way
which cannot be easily generalized to higher dimension. The aim of this paper
is to present an elementary discussion of the Peierls argument for the general
$D$-dimensional Ising model.
