Percus–Yevick type approximations and the Ising model

For the Ising model with short range, approximations similar to the Percus–Yevick approximation are constructed. It is shown that among them one can select a complete class of approximations, call Percus–Yevick type approximations, which can be solved exactly. Near the critical point, the solution thus obtained gives the classical values of the critical indices. It is shown that one can readily construct an approximation of the Percus–Yevick type with an equation of state satisfying the scaling hypothesis.