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There have been a lot of methods aimed at studying the limiting free energyper particle (LFEPP) for 3D Ising model in absence of an external magneticfield. These methods are elegant, but most of them are complicated and oftenrequire specialized knowledge and special skills. Here we approximate the LFEPPfor Ising model from its corresponding functional integral, in which only thegeneral knowledge of mathematical analysis, linear algebra and asymptoticcomputation is used. The resulting Ising LFEPP, which is expressed in terms ofan integral including a special function, is exact asymptotically. From thisintegral expression, we further get a simplified LFEPP, in which only oneparameter needs to be determined. The simplified LFEPPs in two limiting casesfor 1D and 2D Ising model are consistent or formally consistent with thosewell-known, respectively. Based on these consistences, we infer the LFEPPs for3D model in these special cases. Furthermore, we suggest similar LFEPPs for1D-3D Ising models with an external magnetic field, although they are toocomplicated.

Limiting free energy per particle for Ising Model by approximating its functional integral