High Temperature Series Expansions for Spin- and Spin-Phonon-Systems

In this thesis the thermodynamical properties of spin- and spin-phonon-systems are investigated. In the first part of the thesis pure spin-1/2 models are addressed: the dimerized, frustrated chain, the ladder with cyclic exchange, and the two-dimensional Shastry-Sutherland model. The second part presents results for a spin-1/2 system coupled to lattice vibrations, i.e. phonons. By means of high temperature series expansions quantities like the magnetic susceptibility and the specific heat are calculated. These quantities are in most cases easily accessible experimentally. The obtained truncated series have the full dependence of the model parameters. Thus, fitting procedures become a fast and easy task. The coefficients of the truncated series are given as fractions of integers such that no accuracy is lost. The results are exact up to the given order. To improve the representations of the results extrapolation techniques are applied, namely Padé and Dlog-Padé extrapolations. The extrapolations are stabilized in the low temperature region using well-known information on the T=0 and on the low temperature behavior. The extrapolated series expansion results are gauged carefully by investigating their convergence and by comparing them to numerical data obtained from other methods like exact complete diagonalization, quantum Monte-Carlo, and transfer matrix-renormalization group. For the dimerized, frustrated spin system the difficulty is discussed to extract more than two coupling constants from the temperature dependence of the magnetic susceptibility. The ladder system is extended by the inclusion of a four-spin (cyclic) exchange. The impact of this new type of interaction is investigated. Comparison to experimental data of the ladder system SrCu2O3 shows, that the ladder model with a significant but small amount of cyclic exchange can serve as a description of the experimental data just as well as a pure ladder model. The inclusion of cyclic exchange leads to more realistic values for the coupling constants than the values obtained from fitting the ladder model without this type of exchange. The two-dimensional Shastry-Sutherland model has a realization in the compound SrCu2(BO3)2 allowing a detailed comparison between theory and experiment. The three-dimensionality of the substance is explicitly taken into account in the calculations using a mean-field like ansatz for the inter-layer coupling. The extrapolations of the high temperature series data can reproduce the experimental susceptibility data down to very low temperatures. The explicit calculations for the spin-1/2 system coupled to dispersionless phonons are performed using the cluster expansion technique. No cut-off in the phonon subspace is necessary such that the full phonon dynamics are taken into account. The influence of the additional coupling to the phononic degrees of freedom is addressed concerning the magnetic susceptibility and the specific heat