Thermodynamic behaviour of the Heisenberg ferromagnet

The finite temperature perturbation formalism, developed for the spin ½ Heisenberg model in the preceding paper, is applied under high-density conditions. The diagrams arising in the expansion for the temperature-dependent Green function are classified at finite temperatures with respect to the high-density parameter 1/ z , where z is the number of spins interacting with a given spin. The results of molecular field theory are found in first order. The next two orders are considered in detail at low temperatures where they yield respectively spin-wave theory and Dyson's results in the first Born approximation to the scattering of spin waves. The high-density classification, previously justified only for T / T c > 1/ z is directly verified at low temperatures. Higher-order graphs are found to yield at low temperatures the expressions given originally by Tahir-Kheli and ter Haar for the lifetimes of the excitations.