We have generalized the linked cluster expansion method to solve more many-body quantum systems, such as quantum spin systems with crystal-field potentials and the Hubbard model. The technique sums up all connected diagrams to a certain order of the perturbative Hamiltonian. The modified multiple-site Wick reduction theorem and the simple $\tau$ dependence of the standard basis operators have been used to facilitate the evaluation of the integration procedures in the perturbation expansion. Computational methods are developed to calculate all terms in the series expansion. / As a first example, the perturbation series expansion of thermodynamic quantities of the single-band Hubbard model has been obtained using a linked cluster series expansion technique. We have made corrections to all previous results of several papers (up to fourth order). The behaviors of the three dimensional simple cubic and body-centered cubic systems have been discussed from the qualitative analysis of the perturbation series up to fourth order. We have also calculated the sixth-order perturbation series of this model. / As a second example, we present the magnetic properties of spin-one Heisenberg model with arbitrary crystal-field potential using a linked cluster series expansion. The calculation of the thermodynamic properties using this method covers the whole range of temperature, in both magnetically ordered and disordered phases. The series for the susceptibility and magnetization have been obtained up to fourth order for this model. The method sums up all perturbation terms to certain order and estimates the result using a well-developed and highly successful extrapolation method (the standard ratio method). The dependence of critical temperature on the crystal-field potential and the magnetization as a function of temperature and crystal-field potential are shown. The critical behaviors at zero temperature are also shown. The range of the crystal-field potential for Ni(2+) compounds is roughly estimated based on this model using known experimental results. / Source: Dissertation Abstracts International, Volume: 53-03, Section: B, page: 1445. / Major Professor: Yung-Li Wang. / Thesis (Ph.D.)--The Florida State University, 1992.

The number of Frenkel pairs produced per ion (N(,FP)) was measured at 5K for various heavy ion irradiations of thin chromium films. Values much lower than those predicted by transport theory were found. The divergence of experiment and theory was correlated with the maximum elastic deposited energy density ((THETA)(,M)) and the average concentration of Frenkel pairs (C(,FP)). Subthreshold recombination is the only mechanism that can explain why N(,FP)(Exp) was less than unity for several of the irradiations. / For a given ion mass the rate at which the damage annealed out of the chromium films dependent on the irradiation energy. The difference between the annealing rates of 20 and 100 keV ion induced damage was most prominent for the heavier masses (I+,Br+). The presence of unannealed damage at 80K suggest that at least some clustering of defects did occur. / For the 20-50 keV/atom range N+ and N(,2)+ ions of equal velocities had the same defect production rate. No difference in the annealing rates of the damage from these two beams was detected. It is speculated, however, that a higher mass atom would have different damage rates (per atom) associated with its monomer and dimer ions of equal velocity. / Source: Dissertation Abstracts International, Volume: 47-05, Section: B, page: 2045. / Thesis (Ph.D.)--The Florida State University, 1986.

The linked-cluster series expansion is developed fur use on models of quantum spin systems with single-ion potentials. The linked-cluster series is defined as a statistical mechanical perturbation series in which the mean-field Hamiltonian and the single-ion potential are treated exactly with the perturbation representing the effects of fluctuation correlations. All terms of the free energy up to a given finite order are calculated, and estimates of thermodynamic functions are made based on extrapolation methods including the ratio method and Pade approximants. / The T-integrals which the theory requires to be calculated are done with the use of a Wick theorem. Software for doing this algebraic integration procedure by computer is described. / As an example of the technique a sixth order free energy series for the anisotropic Heisenberg exchange model with D(S('z)(,i))('2) single-ion potential has been calculated. Equilibrium properties over the entire temperature range for a fcc lattice are estimated including magnetization versus temperature and susceptibility versus temperature curves. Phase diagrams for selected values of exchange anisotropy are produced. Magnetization and susceptibility exponents are estimated. Tricritical points in the D-T plane are obtained for selected values of exchange anisotropy. The value of exchange anisotropy for hard-axis values of D above which bicritical behavior is seen is estimated. / Source: Dissertation Abstracts International, Volume: 47-06, Section: B, page: 2499. / Thesis (Ph.D.)--The Florida State University, 1986.

Niobium films (120 nm thick) deposited by electron-beam evaporation were implanted near 5 K with 100 keV N(,2)('+) ions to maximum fluences of 4 to 7 x 10('17) N/cm('2). STEM diffraction patterns showed a structural phase transformation from the initial Nb lattice with 110 fiber texture (bcc, a(,o) = 3.30 (ANGSTROM)) to randomly oriented (delta)-NbN (fcc, a(,o) = 4.35-4.39 (ANGSTROM)), via an intermediate, highly disordered Nb-(interstitial N) structure (bcc, maximum a(,o) = 3.42 (ANGSTROM)). Decreases in transition temperature T(,c) from 9 K to a minimum of 3 K, and rapid linear increases in residual resistivity (rho)(,10), were observed to fluences of 1.0-1.5 x 10('17) N/cm('2), and were attributed to the accumulation of radiation-induced defects. Continued implantation resulted in (delta)-NbN formation and T(,c) increases to maximum values of 9-10 K which were achieved at fluences from 3.5 to 5.0 x 10('17) N/cm('2), corresponding to average substoichiometric N/Nb ratios of 0.52-0.75, at which point the phase transformation was complete. The (delta)-NbN formation was accompanied by significant lattice reordering and grain growth. At higher fluences, gradual T(,c) declines (by 1-2 K), and the sharp rises in (rho)(,10), were observed, possibly due to film sputtering. Large reductions in flux pinning force density F(,P) to fluences which produced minimum T(,c) values (about 1 x 10('17) N/cm('2)) were attributed to the destruction of strong grain boundary pinning centers by the ion bombardment. Substantial recovery of F(,P) to levels below the initial values occurred at higher fluences, probably due to the grain recrystallization and larger upper critical fields H(,c2) (H(,c2)(O) (TURN) 75-110 kOe) of the (delta)-NbN phase. / Source: Dissertation Abstracts International, Volume: 46-04, Section: B, page: 1226. / Thesis (Ph.D.)--The Florida State University, 1985.

By using a temperature measurement, the magnetic field induced dissipation in polycrystalline YBa$\sb2$Cu$\sb3$O$\sb{\rm x}$ at T $<<$ T$\sb{\rm c}$ has been measured for magnetic fields up to 2970 Oe applied at constant ramp rates, in the absence of a transport current. The B-H hysteretic behavior has been simultaneously measured so a comparison of the dissipation measured by magnetization to that of thermal dissipation could be determined. Results show that at low temperatures (4.2-8 K) the thermal measurement is very sensitive (dissipation energies of a fraction of an erg/cm$\sp3$ in a 60 hz bandwidth can be sensed) and may provide a superior method in determining dissipation state properties for high temperature superconductors. The dissipation and magnetization results have been modeled using a classical eddy current mechanism, a Rayleigh-Bean model, and Preisach's hysteresis model. No single model described all of the dissipation data. However, at low fields in nonvirgin runs the classical eddy current model roughly described the data, but for high fields in virgin runs the Rayleigh-Bean and Preisach model described the data. / We also report the observation of magnetocaloric cooling in polycrystalline YBa$\sb2$Cu$\sb3$O$\sb{\rm x}$ at 6.5 and 7.1 K. By using a temperature measurement the field induced cooling in an adiabatic environment has been measured for magnetic fields up to 500 Oe applied at constant ramp rates. The cooling is proportional to the square of the applied field and independent of the ramp rate of the magnetic field. Using classical thermodynamic arguments we find that 0.001-0.0045% of the material has returned to the normal state in an applied field of 100 Oe at 7.1 K, and that the field dependence is consistent with a quantized flux lattice. / This experiment is unique; it is the first thermal measurement of the magnetic field induced dissipation in YBa$\sb2$Cu$\sb3$O$\sb{\rm x}$ or any other high T$\sb{\rm c}$ compound. / Source: Dissertation Abstracts International, Volume: 52-06, Section: B, page: 3133. / Major Professor: Louis R. Testardi. / Thesis (Ph.D.)--The Florida State University, 1991.

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.