On the spontaneous magnetization in the Ising model

The equality between the spontaneous magnetization and the long range order is established for the Ising model with nearest neighbour interactions for low and high temperatures. The proof is presented for the two-dimensional lattice but works also in higher dimensions. The result verifies that the valuem*=(1–(Sh)^–4)^1/8 of the spontaneous magnetization below the critical point calculated by Onsager and Yang is the true value, which has been a long standing open question.