Second order transitions are classified by their critical exponents,
which measure how quantities diverge at the critical point.
N.B. These are asymptotic results.
In many cases, these exponents () are universal, i.e., they do not depend on details of the model, but only on gross features such as the dimension of the space and the symmetries of the energy function. This explains the success of very simple spin models like the Ising model in providing a quantitative description of real magnets with complex interactions.