  In the presence of finite chemical potential $\mu$, we holographically
compute the entanglement of purification in a $2+1$- and $3+1$-dimensional
field theory and also in a $3+1$-dimensional field theory with a critical
point. We observe that compared to $2+1$- and $3+1$-dimensional field theories,
the behavior of entanglement of purification near critical point is different
and it is not a monotonic function of $\frac{\mu}{T}$ where $T$ is the
temperature of the field theory. Therefore, the entanglement of purification
distinguishes the critical point in the field theory. We also discuss the
dependence of the holographic entanglement of purification on the various
parameters of the theories. Moreover, the critical exponent is calculated.
