Formulate the exact solution of the two-particle Ising model with an external ``field'' (assume that each particle can take only two states; σ=−1 or +1). Find both the ``magnetization'' and the energy, and show that there is no phase transition in zero external field. Solve the problem by mean field theory, and show that a transition to a spontaneous magnetization in zero external field is predicted to occur at a non-zero temperature Tc. Show that below Tc the spontaneous moment varies as (T−Tc)β and find Tc and the critical exponent β (recall Chapter 11).