Dipolar interactions of trapped dipolar molecular ions

Abstract: The topic of this thesis is the development of a numerical model of trapped dipolar molecular ions forming a Coulomb crystal, such as in a linear ion trap. The model regards the system as an ensemble of classical dipoles which form a linear chain in one dimension, and a square lattice in two dimensions. The model was simulated using Metropolis Monte Carlo and the classical Heisenberg model with dipole-dipole interaction. The possibility of phase transitions in the system was investigated by studying the thermodynamic properties at different temperatures, finite system sizes, and boundary conditions. Previous studies of isotropic classical Heisenberg models in 1D and 2D have shown the absence of of any phase transitions. The 1D dipolar system modeled in this thesis showed no evidence of a critical temperature related to a phase transition, but rather exhibited a slow transition between an ordered and a disordered state for temperatures T > 0. Similar results were obtained for the 2D system, but in this case a method of finite size analysis suggested the existence of a critical temperature. In both systems the dipoles showed a preferential ordering along the z-axis, corresponding to the trap-axis of the ion trap, at low temperature. The results of the simulations are mostly inconclusive due to difficulties in properly evaluating the critical phenomena, and further improvements and extensions to the preliminary model are needed to get more reliable results.