The temporal evolution of equilibrium fluctuations for surface steps of monoatomic height is analyzed studying one-dimensional solid-on-solid models. Using Monte Carlo simulations, fluctuations due to periphery-diffusion (PD) as well as due to evapor
ation-condensation (EC) are considered, both for isolated steps and steps confined by the presence of straight steps. For isolated steps, the dependence of the characteristic power-laws, their exponents and prefactors, on temperature, slope, and curvature is elucidated, with the main emphasis on PD, taking into account finite-size effects. The entropic repulsion due to a second straight step may lead, among others, to an interesting transient power-law like growth of the fluctuations, for PD. Findings are compared to results of previous Monte Carlo simulations and predictions based, mostly, on scaling arguments and Langevin theory.
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy, the XXZ model, and competing planar single-ion anisotropy in a magnetic field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. The bic
onical (supersolid) phase, bordering the antiferromagnetic and spin-flop phases, is found to become thermally unstable well below the onset of the disordered, paramagnetic phase, leading to interesting multicritical points.
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy, the XXZ model, in a magnetic field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. Analyzing, especially, various staggered susceptib
ilities and Binder cumulants, we present clear evidence for the meeting point of the antiferromagnetic, spin--flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions based on various theoretical approaches.
