An empirical partition function for two-dimensional Ising Model in an\n external magnetic field

There is no an accepted exact partition function (PF) for the two-dimensional\n(2D) Ising model with a non-zero external magnetic field to our knowledge. Here\nwe infer an empirical PF for such an Ising model. We compare the PFs for two\nfinite-size Ising lattices ($4\\times 4$ and $4\\times 6$) from this empirical PF\nwith those from Wei (2018) (Wei, R.Q., 2018. An exact solution to the partition\nfunction of the finite-size Ising Model, arXiv: General Physics: 1805.01366.),\nand find that they are consistent very well. Based on this empirical PF, we\nfurther analyze and calculate the thermodynamic functions (heat capacity,\nmagnetization, susceptibility) of this 2D Ising model and discuss the model's\nsingularity semiquantitatively. Analysis and calculations from this PF show\nthat they are coincident with those from other related studies; Especially the\n2D Ising model in an external magnetic field has spontaneous magnetization (SM)\ncalling the phenomenon at the critical temperature a phase transition, and the\nSM decreases with the increasing temperature. However, the decreasing variation\nof the SM here is different from that obtained by Yang (1952) from the 2D Ising\nmodel in a weak magnetic field.\n