  We study the entanglement of purification (EoP), a measure of total
correlation between two subsystems $A$ and $B$, for free scalar field theory on
a lattice and the transverse-field Ising model by numerical methods. In both of
these models, we find that the EoP becomes a non-monotonic function of the
distance between $A$ and $B$ when the total number of lattice sites is small.
When it is large, the EoP becomes monotonic and shows a plateau-like behavior.
Moreover, we show that the original reflection symmetry which exchanges $A$ and
$B$ can get broken in optimally purified systems. In the Ising model, we find
this symmetry breaking in the ferromagnetic phase. We provide an interpretation
of our results in terms of the interplay between classical and quantum
correlations.
