The critical behavior of the classical D-dimensional spin model (D${ge}$2), which is intermediate model that link up the Ising (D = 1) and the spherical model (D = ${infty}$), is studied for the case of constant coupling interaction independent of the spin-spin distance (Curie-Weiss model). Analytical results show that the critical behavior of the present model is in quantitative agreement with the prediction of the phenomenological mean-field theory independent of D. Critical temperature is calculated to be T$_c$=k/JD. This gives a quantitative explanation of the relationship between the spin degree of freedom and the critical temperature.