The Exact Diagonalization method is a powerful numerical tool to study Quantum Many Body systems on finite clusters. In particular, using this technique one can accurately calculate energy and momentum dependent dynamic correlation functions which are observable in scattering experiments, such as Neutron Scattering, Raman Scattering, and Photoemission Spectroscopy which measures the spectral function of the system. Here we give an outline of the Lanczos method with special emphasis on the evaluation of dynamical quantities. / In this thesis, we apply this method to two-dimensional models of strongly correlated electrons which are believed to describe the physics of the recently discovered cuprate high-$\rm T\sb{c}$ compounds. We show that simple models of strongly correlated electrons, such as the Hubbard and the t-J model, can account for some normal state properties of these materials. In particular, the occurance of photoemission bands which are introduced by short-range antiferromagnetic correlations is discussed. / The precursor materials of the cuprate superconducters are antiferromagnets. Here, we address the properties of antiferromagnets as they evolve from an insulating to a metallic phase upon doping. We focus on the shape of the Fermi surface at small hole doping and on the influence of long-range Coulomb interactions on the occurance of superconducting and charge density wave phases. / We also investigate systems in one spatial dimension where mechanisms similar to the ones in higher dimensions can be studied on larger clusters. However, there are some significant dimension dependent differences, e.g. in contrast to the two-dimensional case, one-dimensional antiferromagnets exhibit a gapped spectrum if the participating spins have integer value. We discuss the physics of these 'Haldane' chains. The calculated spectra for these materials are in excellent agreement with recent Neutron Scattering Experiments. / The effect of random exchange interaction in quantum antiferromagnets is also discussed. We show that such interactions do not necessarily induce an exponential decay in the spin correlations. Also, we argue that random exchange interactions can be induced by phononic disorder and might be responsible for the lineshape of Raman spectra observed in the cuprates. Our calculated Raman spectra are in good agreement with recent experiments on various cuprate precursors. / Source: Dissertation Abstracts International, Volume: 56-07, Section: B, page: 3828. / Major Professor: E. R. Dagotto. / Thesis (Ph.D.)--The Florida State University, 1995.

Transfer-matrix and finite-size scaling methods are applied to two different lattice-gas models to elucidate equilibrium and nonequilibrium aspects of first-order phase transitions in systems with interactions of finite range. / The first model is derived from the anisotropic (asymmetric) next-nearest-neighbor interaction (ASYNNNI) lattice-gas model which describes the structural phase transitions of the high-temperature superconductor YBa$\sb2$Cu$\sb3$0$\sb{6 + x}$ in terms of second-order phase transitions in the CuO basal planes. To account for experiments indicating that these transitions might be first-order at low temperatures, we extend the ASYNNNI model to include weak attractive anisotropic interactions between next-nearest-neighbor oxygen chains. Using the conventional transfer-matrix method and finite-size scaling, we calculate the equilibrium phase diagram and find first-order phase transitions and tricritical points at low temperatures for the order-order as well as the order-disorder transitions. / The second model is the two-dimensional square-lattice nearest-neighbor Ising ferromagnet. We study the metastability displayed by this model below its critical temperature and in an external field. Applying a constrained-transfer-matrix formalism, we obtain complex-valued constrained free energies. In particular, we study the imaginary part of the constrained free-energy branch that corresponds to the metastable phase. Although droplets are not introduced explicitly, the metastable free energy is obtained in excellent agreement with field-theoretical droplet-model predictions. The finite-size scaling properties are different in the weak-field and intermediate-field regimes, and we identify the corresponding different critical-droplet shapes. Our results extend the region of validity for known results of the field-theoretical droplet model, and they indicate that this transfer-matrix approach provides a nonperturbative numerical continuation of the equilibrium free energy into the metastable phase. / Source: Dissertation Abstracts International, Volume: 55-11, Section: B, page: 4917. / Major Professor: P. A. Rikvold. / Thesis (Ph.D.)--The Florida State University, 1994.

Source: Dissertation Abstracts International, Volume: 29-02, Section: B, page: 0734. / Thesis (Ph.D.)--The Florida State University, 1967.

Source: Dissertation Abstracts International, Volume: 31-09, Section: B, page: 5561. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 31-09, Section: B, page: 5564. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 31-09, Section: B, page: 5564. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 31-11, Section: B, page: 6830. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 32-01, Section: B, page: 0507. / Thesis (Ph.D.)--The Florida State University, 1970.

Source: Dissertation Abstracts International, Volume: 30-12, Section: B, page: 5654. / Thesis (Ph.D.)--The Florida State University, 1969.

Source: Dissertation Abstracts International, Volume: 30-02, Section: B, page: 0807. / Thesis (Ph.D.)--The Florida State University, 1968.