  There have been a lot of methods aimed at studying the limiting free energy
per particle (LFEPP) for 3D Ising model in absence of an external magnetic
field. These methods are elegant, but most of them are complicated and often
require specialized knowledge and special skills. Here we approximate the LFEPP
for Ising model from its corresponding functional integral, in which only the
general knowledge of mathematical analysis, linear algebra and asymptotic
computation is used. The resulting Ising LFEPP, which is expressed in terms of
an integral including a special function, is exact asymptotically. From this
integral expression, we further get a simplified LFEPP, in which only one
parameter needs to be determined. The simplified LFEPPs in two limiting cases
for 1D and 2D Ising model are consistent or formally consistent with those
well-known, respectively. Based on these consistences, we infer the LFEPPs for
3D model in these special cases. Furthermore, we suggest similar LFEPPs for
1D-3D Ising models with an external magnetic field, although they are too
complicated.

Statistical Mechanics