Problem 7.15. In the mean field approximation to the Ising lattice, the order parameter, (s), satisfies the equation (s) = tanh((s) ), where T = ve/2kg with the strength of the coupling between lattice sites and v the number of nearest neighbors.

(a) Show that (s) has the following temperature dependence: (i) (s) 1-2e-2./T if T~0 K, and (ii) (s)3(1-T/T) if T~T.

(b) Compute the jump in the heat capacity at T=T.

(c) Compute the magnetic susceptibility, XT,N(B = 0), in the neighborhood of T=T_c for both T> Te and T < t_{c .} what is the critical exponent of both cases ?