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.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_75839 |
| Contributors | WENTWORTH, CHRISTOPHER DEAN., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 270 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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