This thesis is about the magnetic properties of two different two dimensional systems. The first one corresponds to vanadates or cuprate crystals, which can be studied by a spin system on square lattice and a Heisenberg model with three couplings, a ferromagnetic first neighbor coupling and antiferromagnetic second and third neighbor couplings. This system is frustrated and lead to a non trivial classical phase diagram. We have studied the influence of quantum fluctuation using a Holstein-Primakov approach and the Schwinger bosons model. The second system studied corresponds to graphene of finite size. To study this system we use a mean field approximation of the Hubbard model. In a first step we recover within our method well known results and check that the model has been correctly implemented. In a second step, in order to assess the accuracy of this method, we perform complementary exact diagonalization calculations, and compare our results with quantum Monte Carlo simulations. And in the last part we will show evidence of a dynamical signature of the zigzag edge magnetization of finite sample of graphene.
