Stoffel, AndreGulacsi, Miklos2015-12-101478-6435http://hdl.handle.net/1885/60079We solve in the random-phase approximation the anisotropic Heisenberg model, including nearest and next-nearest neighbour interactions by calculating all the Green's functions and pair correlation functions in a cumulant decoupling scheme. The general exposition is pedagogic in tone and is intended to be accessible to any graduate student or physicist who is not an expert in the field. To Jim 'Think where man's glory most begins and ends, And say my glory was I had such friends.' 1 From Miki.Keywords: Anisotropic Heisenberg models; Bose condensation; Cumulants; Graduate students; Many-body theory; Nearest-neighbour interactions; Pair correlation functions; Random phase approximations; Anisotropy; Condensation; Differential equations; Ground state; Gree Bose condensation; Many body theory; Theoretical200910.1080/147864309029738662016-02-24