A Matter of Disorder : Monte Carlo Simulations of Phase Transitions in Strongly Disordered Systems

Abstract: Phase transitions and their critical scaling properties, especially in systems with disorder, are important both for our theoretical understanding of our environment, but also for their practical use in applications and materials in our everyday life. This thesis presents results from finite size scaling analysis of critical phenomena in systems with disorder, using high-precision Monte Carlo simulations and state of the art numerical methods. Specifically, theoretical models suitable for simulations in the presence of uncorrelated or correlated disorder are studied. Uncorrelated strong disorder, as present in the two dimensional gauge glass model to study the vortex glass phase of high temperature superconductors in an applied magnetic field is shown to lack a finite temperature phase transition. Further, results from dynamic quantities, such as resistance and autocorrelation functions, indicate the existence of two distinct diverging correlation times, one associated with local relaxation and one associated with vortex phase slips. Correlated disorder is studied both in the superfluid transition of helium-4 and in the anisotropic critical scaling of a transverse Meissner-like transition in an experimental setup of a high temperature superconductor. For the superfluid helium transition, it is shown that the presence of fractally correlated disorder presumably alters the universality class of the pure model. Also, a comparison with experimental data suggests that the critical scaling theory describing the heat capacity of helium-4 may need to be modified in the presence of the disorder. In the case of superconductors, analyzing experimental data from resistance measurements in a system with columnar defects together with an anisotropy in the applied magnetic field, reveals a fully anisotropic scaling regime. Finally, a data analysis is presented from simulations of a charged particle gas system in three dimensions, where the normal Coulomb interaction between charges is changed into a logarithmic interaction. Previous work indicates the possibility of a transition similar to the Kosterlitz-Thouless transition in certain two dimensional systems. On the contrary, our simulations seem to favor a system whose critical scaling behavior is consistent with a transition occurring only at zero critical temperature. Overall, disorder in the model systems studied leads to important modifications of the critical scaling properties of pure systems, and thereby also to possible changes of the corresponding universality classes. This results in interesting predictions with experimentally relevant consequences.