S trongly correlated magnetic systems have recived graet attention in recent years because of their remarkable properties. But due to the complexity of such systems, our understanding of their unfamiliar observed properties is still incomplete. One of these interesting phenomena is frustration. A frustrated system remains disorderd at temperatures much less than Curie Weiss temperature. Ground state manifold of this system is macroscopically degenerate and this degenerate ground state is very sensitive to perturbations. In this thesis by concentrating on frustrated systems, we use some magnetic models to study Bravias and none- B ravias lattices. As a first step in modelling frustrated magnets, we introduce the normal" J 1 -J 2 Heisenberg model in honeycomb and diamond lattices. This model on bipartite lattice exhibits Neel ordering. However if the AF interactions between the next nearest neighbor() are increased with respect to the nearest neighbor(nn), the frustration effect arises. In such situations, new phases such as ordered phases with coplanar or spiral ordering and disordered phases such as spin liquids appear. Here, we find the spin liquid phases such as ring-liquid and pancake-liquid in honeycomb lattice. Also, fordiamond lattice we show that the degeneracy of ground state can be lifted by thermal fluctuations through the order by disorder mechanism.
