The two-dimensional t-J model on the square lattice is studied as a relevant model to capture the essential physics of the high-temperature copper-oxide superconductors. In order to gain understanding of the basic physics of the model, fundamental issues such as the motion of a single hole and the binding of two holes in a quantum antiferromagnet are addressed. A numerical approach is followed, combining a variation calculation with the use of the Green's function Monte Carlo method, applied in this thesis for the first time to study the t-J model in the presence of mobile holes. Important insight is obtained on the effect of a single hole on the antiferromagnetic background and on the occurrence of binding of two holes. It is found that a critical value $(t/J)\sb{c}$ of the parameter t/J of the model exists such that hole binding no longer takes place for $t/J>(t/J)\sb{c},$ with $(t/J)\sb{c}\sim3.7.$ The value that t/J should have in the real material is estimated to be about 3, in order for the model to be relevant to superconductivity. Further research developments are discussed. / Source: Dissertation Abstracts International, Volume: 53-10, Section: B, page: 5271. / Major Professor: Efstratios Manousakis. / Thesis (Ph.D.)--The Florida State University, 1992.

Source: Dissertation Abstracts International, Volume: 41-01, Section: B, page: 0250. / Thesis (Ph.D.)--The Florida State University, 1980.

A new approach to the high-temperature series expansion which is applicable to systems with complicated energy level schemes such as magnetic systems with crystal-field anisotropy of arbitrary strength has been formulated. We compare this approach with the original Green's function formulation of Wand and Lee and discuss the advantage of the present technique. We apply the approach developed here to the spin-one hard-axis Heisenberg ferromagnet and obtain the first four terms in the high-temperature series expansion for the free energy, the magnetic susceptibility, and the specific heat. The formula obtained for the free energy of the spin-one hard-axis ferromagnet also describes spin-one systems with rhombic anisotropy and reduces to the spin-one ferromagnet with an easy-axis anisotropy and to the spin-one simple Heisenberg systems by setting the appropriate matrix elements equal to zero. The method can be extended to treat systems with spin greater than one with general crystal field symmetry. The calculation of higher order terms is rendered tractable using the approach developed here. / Source: Dissertation Abstracts International, Volume: 41-02, Section: B, page: 0612. / Thesis (Ph.D.)--The Florida State University, 1980.

Source: Dissertation Abstracts International, Volume: 41-09, Section: B, page: 3493. / Thesis (Ph.D.)--The Florida State University, 1980.

Fe$\sb3$O$\sb4$ (magnetite) is a ferromagnetic semiconductor while NiO is an antiferromagnetic insulator with a room temperature resistivity at least six orders of magnitude greater than that of Fe$\sb3$O$\sb4.$ Modulated structure films, with equal Fe$\sb3$O$\sb4$ and NiO layer thicknesses, were grown using plasma assisted molecular beam epitaxy to a total film thickness of 3446A, and with modulation wavelengths $\Lambda$ (bilayer thicknesses) ranging from 16A to 1763A. Post growth $\theta$-2$\theta$ x-ray data contain well defined low angle peaks which confirm that the targeted layer thicknesses were accurately achieved. Resistivity has been measured perpendicular to the plane of the film, as a function of modulation wavelength and temperature. A dependence of the resistivity on $\Lambda$ is observed in two sample sets in which the resistivity rapidly increases many orders of magnitude as the modulation wavelength decreases from the bulk $\Lambda\rightarrow\infty$ limit in the vicinity of 600A. This length scale dependent resistivity enhancement of the Fe$\sb3$O$\sb4$/NiO modulated structures cannot be explained by the standard model of interfacial resistance. A qualitative argument is presented for a metal-insulator-metal interfacial charge transfer model which contains both the resistivity enhancement and the observed length scale dependence. / Source: Dissertation Abstracts International, Volume: 57-04, Section: B, page: 2634. / Major Professor: L. R. Testardi. / Thesis (Ph.D.)--The Florida State University, 1996.

Analytical and numerical methods are used to study the stationary properties of equilibrium and metastable phases in scalar field theories and model systems with weak, long-range forces (WLRF) by determining the finite-range scaling (FRS) of the free energy F and its analytic continuation $\tilde F$ into the metastable phase. The scaling properties of d-dimensional $\phi\sp n$ scalar field theories are derived, and two special cases are used to study equilibrium and non-equilibrium critical phenomena in WLRF systems. A criterion of critical equivalence is identified, relating the FRS of WLRF systems to the finite-size scaling of hypercylindrical systems above the upper critical dimension. A method of analytically continuing the equilibrium free energy into the metastable phase is generalized for systems exhibiting multiple metastable phases, and new scaling results for $\tilde F$ are found near classical spinodals, including exact results for $d=1.$ An analytic continuation of the free energy is performed numerically on two hypercylindrical systems and compared to analytic expansions for equivalent field theories. Transfer-matrix (TM) finite-size scaling confirms the critical exponents for $d=1$ WLRF systems. For metastable phases, a constrained-transfer-matrix (CTM) method is applied, in which one obtains a "constrained" free-energy density computed directly from the TM. Monte Carlo simulation is performed to obtain decay rates directly, which are compared with both the CTM results and the analytic continuation using Langer's proportionality relation. / Source: Dissertation Abstracts International, Volume: 56-01, Section: B, page: 0316. / Major Professor: Per Arne Rikvold. / Thesis (Ph.D.)--The Florida State University, 1994.

We numerically investigate the finite-size scaling properties of the superfluid density and of the specific heat of superfluid $\sp4He$ confined in cubic and film geometries by using the $x - y$ model and the Cluster Monte-Carlo method. We show that the superfluid density and the specific heat of $\sp4He$, confined in a cubic geometry, scale with respect to the linear length of the system according to finite-size scaling theory, and we derive the temperature dependence of these quantities in the bulk limit by extrapolating the values of the superfluid density and the specific heat obtained for finite lattices to the values corresponding to a lattice of infinite extent. In the case of the film geometry, $\sp4He$ exhibits a Kosterlitz-Thouless phase transition at the thickness-dependent critical temperature, i.e., close to this temperature superfluid helium behaves effectively two-dimensional. We show that the boundary conditions imposed in the top and bottom layers of the film strongly influence the shape of the universal scaling functions of the superfluid density and the specific heat with respect to the film thickness. We always compare our results to the experiments. / Source: Dissertation Abstracts International, Volume: 56-04, Section: B, page: 2111. / Major Professor: Efstratios Manousakis. / Thesis (Ph.D.)--The Florida State University, 1995.

The numerical calculation of the partition function of the 3d Ising model and the 2d XY model are performed using the newly developed Spectral Density method. The performance and utility of the method are also shown. The finite size scaling of the complex zeros of the partition function is used to estimate the critical exponent $\nu$ for the two models. Good estimates of $\nu$ exist for the 3d Ising model and are found to agree with the estimates calculated here. Recently, there has been debate over whether the XY model has an infinite order phase transition as previously believed or a finite order transition. The critical exponent $\nu$ is sensitive to this question. Unlike a finite order transition, it is impossible to define $\nu$ for an infinite order transition. It is shown that if estimates of $\nu$ are measured for an infinite order transition, the estimates will diverge in the thermodynamic limit. The nature of the XY model's phase transition is explored by finding estimates of $\nu$ and the behavior of the derivatives of the free energy; however, the results are inconclusive. / Source: Dissertation Abstracts International, Volume: 50-08, Section: B, page: 3549. / Major Professor: Dennis W. Duke. / Thesis (Ph.D.)--The Florida State University, 1989.

The alkali halide surfaces were the first for which full surface phonon dispersion curves were measured. Most of the early work was mainly concerned with the low-energy modes for the lighter alkali halides, such as LiF and NaF, and a full survey of a more representative sampling of these crystals was never made. A recent theoretical calculation has also suggested that relaxation effects might provide interesting features on the surface phonon modes especially for the optical modes of the heavier compounds. The work of this dissertation is an effort to measure the surface dynamics of other, usually heavier, alkali halide crystals. This work describes measurements on the surfaces of RbCl(001), RbBr(001), KBr(001), and NaI(001) with the inelastic He atom scattering technique. The energy gain or loss and the momentum change is measured by the time of flight method. For the four crystals, the surface phonon dispersion curves are obtained along both high symmetry directions. The general agreement between the theory and the experimental results is very good. Some new features of the surface vibration have been found. First, the optical mode, crossing resonance and acoustic modes were clearly seen from the KBr surface over the entire zone. The strong interaction coupling between the He and the optical mode is rather unique. Secondly, crossing resonances (S$\sb8$ mode) were observed for the KBr, RbBr and NaI surfaces. This observation suggests that this mode is a general feature of all the alkali halide surfaces. The origin of this mode might be due to the perpendicular polarized bulk acoustic motion. Thirdly, NaI results show that bound-state resonance effects could strongly enhance the bulk mode especially when there is a high density of phonon states. Finally, there is no experimental evidence supporting any surface relaxation effects. In fact, the experimental / results seem to agree better with the unrelaxed calculations. In addition to the inelastic scattering measurements, we also did angular distribution, low pressure He beam scattering and a temperature-dependent dynamical study. Information such as the surface corrugation, He-surface potential, bound state energies, the surface Debye-Waller temperature and a measure of multi-phonon contributions can be obtained from these experimental results. / Source: Dissertation Abstracts International, Volume: 51-01, Section: B, page: 0266. / Major Professor: J. G. Skofronick. / Thesis (Ph.D.)--The Florida State University, 1989.

Source: Dissertation Abstracts International, Volume: 40-06, Section: B, page: 2733. / Thesis (Ph.D.)--The Florida State University, 1979.