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There is no an accepted exact partition function (PF) for the threedimensional (3D) Ising model to our knowledge. Mainly based on the connectionbetween the lattice Green function (LGF) for the simple cubic lattice and thatfor the honeycomb lattice, we infer an empirical partition function (EPF) forthe 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, $T$ thetemperature, and $k$ Boltzmann constant). When $\alpha=\sqrt{2}$, this EPF isconsistent well numerically with the result from high temperature expansions byGuttmann and Enting (1993). The specific heat from this EPF approaches infinitynon-logarithmically at the critical temperature $T_c$.$\frac{\epsilon}{kT_c}=\cosh^{-1}[\frac{1}{4} (17-3\sqrt{17})]/2\approx0.277212$, which is greater than 0.221654 from the recent Monte Carlo study.

An empirical partition function for the simple cubic Ising Model with a zero external magnetic field