Almost all known high temperature superconductors are cuprates, which can be suitably modelled by the two dimensional Hubbard model. To understand the interplay of various long range properties as antiferromagnetism and superconductivity, one can calculate the phase diagram of the Hubbard model in the charge density-temperature plane. This analysis is conveniently carried out by means of exact renormalization group equations that we apply in the formalism of the effective average action. For this purpose, we derive an equivalent version of the Hubbard model that takes the form of a Yukawa theory. From this modified model long range order in various channels can be extracted by simple calculation of bosonic expectation values. We are able to reproduce the main features of the phase diagram of high temperature superconductors. Furthermore, our analysis shows how the Mermin-Wagner theorem can be reconciled with the existence of antiferromagnetic long range order at non vanishing temperature and how the inclusion of different kinds of bosonic fluctuations affect the phase diagram.