  We calculate thermodynamic potentials and their derivatives for the
three-dimensional $O(2)$ model using tensor-network methods to investigate the
well-known second-order phase transition. We also consider the model at
non-zero chemical potential to study the Silver Blaze phenomenon, which is
related to the particle number density at zero temperature. Furthermore, the
temperature dependence of the number density is explored using asymmetric
lattices. Our results for both zero and non-zero magnetic field, temperature,
and chemical potential are consistent with those obtained using other methods.
