Onset of long-range order in a paramagnet

The onset of long-range order in a paramagnet is studied using an expansion in powers of 1/z, where z is the number of nearest neighbors. Rather than expand the correlation function itself, we expand the self-energy in powers of 1/z. For both the Ising and Heisenberg models of ferromagnetism, the long-range correlations diverge at the true, shifted Curie temperaure. Therefore, the magnetic and paramagnetic results of the 1/z expansion are consistent.