Jan Fivez

On the continuum limit of a classical compressible Heisenberg chain

The author derives the equations of motion for the classical compressible Heisenberg chain in the continuum limit to lowest non-trivial order in the derivatives. It is possible to eliminate the translations from the equation for the spins. The resulting equation does not admit of simple magnetic solitary wave solutions, in contradiction to the results of other authors.

Dynamics of NaNO2 in the paraelectric and in the incommensurate phase

On the basis of a microscopic model with translation-rotation coupling, a set of coupled dynamic equations is derived. The corresponding resonances are studied in the paraelectric and in the incommensurate phase. The theory gives a qualitative explanation of inelastic neutron scattering results.

Monte Carlo Study of the Two-Dimensional Spin-1/2 XY Model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto a three-dimensional Ising model with complicated many-spin interactions. This relationship is used to construct an efficient Monte Carlo algorithm. Simulation data for the specific heat and vortex correlation functions give strong evidence for the existence of a phase transition.

TWO-DIMENSIONAL CLASSICAL REPRESENTATIONS OF THE PARTITION-FUNCTION OF THE SPIN-1/2 CHAIN

Starting from the Trotter formula, we derive several classical representations of the partition function of a spin-1/2 chain. We investigate the rate of convergence of the different approximants by means of exact calculations for small systems. We demonstrate that it is important to use approximants that have the same symmetry properties as the original quantum model.

Librational and relaxational motion of molecular impurities in crystals

The dynamics of a single impurity with rotational degrees of freedom in the static crystal field of the host lattice is revisited. We use numerical simulation techniques to calculate the time-dependent correlation functions accurately up to very long times. Then we carry out a spectral analysis of these results, thus obtaining good estimates for the contribution of different representations to the incoherent scattering cross-sections. For some representations we find non-ergodic behaviour, giving rise to delta-function contributions at zero frequency. In the real crystal these contributions will be broadened because the rotator is coupled dynamically to the phonons of the host crystal, which is not taken into account in our simple model.

Fragility of supercooled liquids from differential scanning calorimetry traces: theory and experiment.

Starting from the Debye model for frequency-dependent specific heat and the Vogel-Fulcher-Tammann (VFT) model for its relaxation time, an analytic expression is presented for the heat capacity versus temperature trace for differential scanning calorimetry (DSC) of glass transitions, suggesting a novel definition of the glass transition temperature based on a dimensionless criterion. An explicit expression is presented for the transition temperature as a function of the VFT parameters and the cooling rate, and for the slope as a function of fragility. Also a generalization of the results to non-VFT and non-Debye relaxation is given. Two unique ways are proposed to tackle the inverse problem, i.e., to extract the fragility from an experimental DSC trace. Good agreement is found between theoretically predicted DSC traces and experimental DSC traces for glycerol for different cooling rates.

Monte Carlo Study of the 2-Dimensional Spin-1/2 XY model

The generalized Trotter formula is used to map the two-dimensional spin-1/2 XY model onto a three-dimensional Ising model with complicated many-spin interactions. This relationship is used to construct an efficient Monte Carlo algorithm. Simulation data give strong evidence for the existence of a phase transition.

Dynamics of a molecular impurity coupled to phonons: Computer simulation

We investigate the classical rotational motion of a molecular impurity in a crystal starting from a model which contains the dynamic coupling of the rotator to the phonons of the host crystal. We use molecular dynamics to simulate the relevant correlation functions. Depending on their symmetry these correlation functions characterize mainly the librational or reorientational motion. The corresponding spectral functions are found by direct Fourier transformation for correlations decaying rapidly in time. The relaxation times of the reorientational motion are very long and have to be estimated from the long time tails of the corresponding time correlations. We find the inverse relaxation time to satisfy an Arrhenius law when the thermal energy is below the potential barrier. This agrees with numerous experimental results and with the ansatz used to stochastic jump models. For high temperatures the inverse relaxation time is proportional to temperature corresponding to rotational diffusion.

Spin-wave modes in a compressible Heisenberg chain of classical spins

The spin dynamics of a compressible chain of classical spins is studied by means of a four pole approximation for the spin relaxation function. The frequency moments are calculated with the help of a computer. The general qualitative influence of the coupling to the phonons on the dynamic structure factor is discussed. Quantitative results for frequency shift, line width and the condition for the observability of spin waves are obtained. Especially the latter is quite different from the result for the rigid Heisenberg chain. The coupling to the phonon degrees of freedom does not lead to additional resonances in the spin spectrum.

Low-temperature spin dynamics of a classical compressible Heisenberg chain

The dynamic spin correlation function of a classical compressible Heisenberg chain is investigated in the low temperature limit. Anharmonic processes, arising from the nonlinearity of the spin equations of motion and from the coupling of the spins to translational degrees of freedom, are taken into account to lowest order. Two-magnon processes and magnon-phonon processes contribute to the spectra. They can give rise to additional resonances but mostly their weight is very small. The main influence of the spin-phonon coupling lies in a change of the width and position of the spin-wave resonance. Comparison is made with previous work.