Application of the Padé Approximant Method to the Investigation of Some Magnetic Properties of the Ising Model

On the basis of the Pad\'e approximant method we deduce from the exact series expansions for the Ising model that the reduced magnetic susceptibility behaves at the critical point as ₅₂₂0. 09923{ (0. 101767-w) }^5{4}, ₁₂₂0. 152773{ (0. 1561789-w) }^5{4}, ₒ₂0. 22138{ (0. 218156-w}^5{4}, ₓ0. 2432{ (2-3-w) }^7{4}, ₒₐ0. 35724{ (2-1-w) }^7{4}, and ₇0. 4506{ (1{3-w) }}^7{4}, where w=tanh (JkT) and the last figure quoted is somewhat uncertain. The spontaneous magnetization is found to behave as ({I₀{I_}) }₅₂₂12. 5 (0. 664658-{z^2) }^0. 3, ({I₀{I_}) }₁₂₂10. 4 (0. 5326607-{z^2) }^0. 3, ({I₀{I_}) }ₒ₂10. 9 (0. 411940-{z^2) }^0. 3, where z=exp (-2JkT) and again the last place quoted is somewhat uncertain. The numbers 54 and 74 have an error of at most 10^-3, and 0. 3 of at most 10^-2. The lattices referred to are fcc, face-centered cubic; bcc, body-centered cubic; sc, simple cubic; t, triangular; sq, simple quadratic; and h, honeycomb.