text: To find , we demand that free energy be zero at  (just like the  solution), and furthermore that this point should be a local minimum. These two conditions yield two equations,
  which are satisfied when . The same equations also imply that . That is,
  From this analysis both points made above can be seen explicitly. First, the order parameter suffers a discontinuous jump from  to 0. Second, the transition temperature  is not the same as the temperature  where  vanishes.
  At temperatures below the transition temperature, , the order parameter is given by
  which is plotted to the right. This shows the clear discontinuity associated with the order parameter as a function of the temperature. To further demonstrate that the transition is first-order, one can show that the free energy for this order parameter is continuous at the transition temperature , but its first derivative (the entropy) suffers from a discontinuity, reflecting the existence of a non-zero latent heat.
  II. Nonsymmetric Case
  Next we consider the case where the system does not have a symmetry. In this case there is no reason to keep only even powers of  in the expansion of , and a cubic term must be allowed (The linear term can always be eliminated by a shift  + constant.) We thus consider a free energy functional