Effect of disorder on the melting phase transition

This Ph.D thesis is concerned with the effect of disorder on the melting phase transition. In the first part, the research is focused on the melting of the flux lines in high temperature superconductors. An analytical approach to studying the effect of quenched disorder on the vortices is proposed. The main steps in proposed approach are drawn from classical thermodynamics. The principal step is to relate a superconductor in the flux line lattice state to a closed system in which two phases are in contact, solid and liquid, with the aim of determining what effect the pinning centres have on the melting temperature. That is to determine whether the melting temperature is raised or lowered with respect to that of the clean non-pinned superconductor. Flux lines are modelled by an elastic Hamiltonian and the quenched disorder by the Larkin pinning Hamiltonian. This analyses is performed for two-dimensional systems as well as three-dimensional ones. The second part of this thesis is concerned with a simulation approach to analysing the melting transition in two-dimension. Joint Molecular Dynamics-Monte Carlo simulations are performed to study the melting transition in two dimensions. Firstly, classical point particles interacting via a r-12 repulsive pair potential are investigated and secondly, disorder is added to this system by introducing randomly positioned attractive pins. In both cases the simulation method chosen is based on the bicanonical ensemble in conjunction with constant temperature molecular dynamics as introduced by H.C. Andersen. Bond orientational order, transitional order, pressure, and the specific heat as well as the potential energy of the system are determined. Histograms of these quantities are obtained throughout the transition region and used together with finite size scaling analysis to deduce t lie nature of the transition by, means of the Lee-Kosterlitz method. For the clean system the r-12 potential is first studied and is chosen for its simplicity in comparison to the full Lennard-Jones potential. The nature of the transition is investigated and the fact that the nature of the transition does riot, change in the temperature-density phase diagram is used. In the disordered case, the particle-pin interaction is given by all attractive Gaussian. Using the same techniques as in the pure case, the effect of disorder on the melting transition is studied. The aim is to make some comparisons with the clean systems transition and find the critical pinning potential at which the transition vanishes completely. Conclusions are drawn front the results of the two-dimensional analytical and the simulation studies of the melting transition ill the presence of disorder. It turns out that it may also be very useful to study the effect of disorder in order to help draw conclusions oil the nature of the transition of the clean system. (author)