On closed-form approximations for the free energy ofd-dimensional Ising model,II

It has been shown that it is possible to construct families of closed-form approximations lnZ* _d to lnZ _d for the anisotropic Ising model on ad-dimensional hypercubical lattice whose high- and low-temperature series expansions coincide with the corresponding exact expansions up to some order. For the isotropic case the density of zeros ofZ* _d near the critical pointK _c is found under the assumption that they behave like sinh2K=±(sinh2K _c +y±iy). It is shown that there exists a family of closed-form approximations such that ford3 the only possible densities of zeros arem(y)=|y|³ for=0 andm(y)=|y| for 0<||1, i.e., it contains the exact case ford5 corresponding to ||=1.