We calculate the magnon modes in the presence of a vortex on a circular system, combining analytical calculations in the continuum limit with a numerical diagonalization of the discrete system. The magnon modes are expressed by the S-matrix for magnon-vortex scattering, as a function of the parameters and the size of the system and for different boundary conditions. Certain quasi-local translational modes are identified with the frequencies which appear in the trajectory X(t) of the vortex center in recent Molecular Dynamics simulations of the full many-spin model. Using these quasilocal modes we calculate the two parameters of a 3 rd -order equation of motion for X(t). This equation was recently derived by a collective variable theory and describes very well the trajectories observed in the simulations. Both parameters, the vortex mass and the factor in front of ··· X, depend strongly on the boundary conditions. 75.10. Hk,75.40.Gb,75.40.Mg,02.60.Cb

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We solve numerically the dissipative Landau-Lifshitz-Gilbert equations to consider hysteresis in fine magnetic particles. Finite size effects are studied for two models with uniaxial anisotropy-bulk random axis and surface anisotropy only. It is demonstrated that the latter model introduces considerable effects for small enough particles when the coupling to the anisotropy is equal or greater than the coupling to the isotropic Heisenberg exchange. We show that some features of magnetization reversal are associated with spins at the surface of fine particles.

The Berezinskii-Kosterlitz-Thouless (BKT) transition in two-dimensional planar rotator and XY models on a square lattice, diluted by randomly placed vacancies, is studied here using hybrid Monte Carlo simulations that combine single spin flip, cluster and over-relaxation techniques. The transition temperature Tc is determined as a function of vacancy density ρvac by calculations of the helicity modulus and the by finite-size scaling of the in-plane magnetic susceptibility. The results for Tc are consistent with those from the much less precise fourth-order cumulant of Binder. Tc is found to decrease monotonically with increasing ρvac, and falls to zero close to the square lattice percolation limit, ρvac ≈ 0.41 . The result is physically reasonable: the long-range orientational order of the low-temperature phase cannot be maintained in the absence of sufficient spin interactions across the lattice.