Calculation of free energies for a three-dimensional Ising model by a modified Kadanoff's variational method

The modified Kadanoff's variational method recently considered by us is applied to calculate the free energies and their derivatives for a three-dimensional Ising model with bcc structure and without external magnetic field. We find a critical point at $k_c=0.162\mathrm{}134$ and the associated critical indices $\alpha =0.12\mathrm{}$, ${\alpha }^{\prime }=0.095\mathrm{}$.