  There is no an accepted exact partition function (PF) for the three
dimensional (3D) Ising model to our knowledge. Mainly based on the connection
between the lattice Green function (LGF) for the simple cubic lattice and that
for the honeycomb lattice, we infer an empirical partition function (EPF) for
the simple cubic Ising model in the absence of an external magnetic field. This
${\rm EPF}_{_{\rm 3D}}=\frac{1}{{2{\pi ^3}}}\int_0^\pi \int_0^\pi \int_0^\pi
\log [2(2{{\cosh }^3}2z + 3{{\sinh }^2}2z + 2)^{\frac{1}{2}} -2\alpha\sinh 2z \
(\cos\omega_1 + \cos \omega_2 + \cos\omega_3)]
{\rm{d}}\omega_1{\rm{d}}\omega_2{\rm{d}}\omega_3, \alpha\in[\sqrt{2},\sqrt{3}]$
(where $z=\frac{\epsilon}{kT}$, $\epsilon$ the interaction energy, $T$ the
temperature, and $k$ Boltzmann constant). When $\alpha=\sqrt{2}$, this EPF is
consistent well numerically with the result from high temperature expansions by
Guttmann and Enting (1993). The specific heat from this EPF approaches infinity
non-logarithmically at the critical temperature $T_c$.
$\frac{\epsilon}{kT_c}=\cosh^{-1}[\frac{1}{4} (17-3\sqrt{17})]/2\approx
0.277212$, which is greater than 0.221654 from the recent Monte Carlo study.
