  There is no an accepted exact partition function (PF) for the two-dimensional
(2D) Ising model with a non-zero external magnetic field to our knowledge. Here
we infer an empirical PF for such an Ising model. We compare the PFs for two
finite-size Ising lattices ($4\times 4$ and $4\times 6$) from this empirical PF
with those from Wei (2018) (Wei, R.Q., 2018. An exact solution to the partition
function of the finite-size Ising Model, arXiv: General Physics: 1805.01366.),
and find that they are consistent very well. Based on this empirical PF, we
further analyze and calculate the thermodynamic functions (heat capacity,
magnetization, susceptibility) of this 2D Ising model and discuss the model's
singularity semiquantitatively. Analysis and calculations from this PF show
that they are coincident with those from other related studies; Especially the
2D Ising model in an external magnetic field has spontaneous magnetization (SM)
calling the phenomenon at the critical temperature a phase transition, and the
SM decreases with the increasing temperature. However, the decreasing variation
of the SM here is different from that obtained by Yang (1952) from the 2D Ising
model in a weak magnetic field.
