Geometrical frustrated systems remain disordered at temperatures much less than Curie-Weiss temperature . It has been understood that the ground state manifold of these systems is macroscopicailly degenerate and this degenerate ground state is very sensitive to perturbations . In this thesis , different types of frustration and also theories of geometrically frustrated systems are considered . The behavior of one frustrated material is studied by using Curie-Weiss law . Since the Coulomb gas occurs only for bipartite lattices , these types of lattices are considered too . Then , parent and medial lattices and study pinch point behavior are defined in these kinds of systems . Self-consistent Gaussian approximation (SCGA) is introduced completely . Also it is explained that how to calculate self-consistent parameter for different temperatures . It is indicated that how to obtain some thermodynamic functions through this method too . Some thermodynamic features for different lattices are considered by using SCGA method : First of all , self-consistent values for simple cubic lattice are found and then structure factor for different wave vectors is shown . Correlation function and magnetic susceptibility are calculated for this lattice too . By calculating susceptibility function , the phase transition temperature and critical exponent of susceptibility is obtained on simple cubic lattice which are compatible with Monte Carlo's simulation results . In addition , structure factor for fcc lattice is calculated , which states that there is no unique maximum in figure of this function . Thus , the effect of weak second-neighbor exchange on the appearance of order in face-centered cubic lattice is studied . Locations of maxima's of the structure factor depend on the type of second neighbor interaction whether it is antiferromagnetic or ferromagnetic one . Moreover , antiferromagnetic Heisenberg model is studied on pyrochlore lattice . The structure factor of this lattice is calculated and shown . It will be obvious that the structure factor has no unique maximum in low temperatures , so that pyrochlore lattice is frustrated . Hence , the anisotropic term is added to the Heisenberg Hamiltonian and its effect on appearing order is considered in this lattice . Finally , XY model on kagome lattice is studied and it has been seen that there is no phase transition in this model . Then the effect of adding anisotropic term to Hamiltonian is considered through SCGA method and phase transition temperature and critical exponent of susceptibility is obtained on simple cubic lattice which are compatible with Monte Carlo's simulation results .
