SCALING AND PATTERN FORMATION IN CONDENSED MATTER SYSTEMS BY

In this dissertation, I present analytical and numerical work regarding the scaling behavior of three physical systems, with increasing levels of complexity. I begin by analyzing the scaling behavior of Griffiths ferromagnets near the Griffiths-paramagnetic transition point. By deriving the asymptotic behavior of the magneti-zation of the system using an ansatz for the Yang-Lee zero density, which is a generic form of the density with the presence of disorder, I find that the scaling behav-ior of Griffiths ferromagnet is completely different from that of conventional (pure) ferromagnets—the scaling is dominated by an essential singularity in the external magnetic field, due to the ferromagnetic response of arbitrarily large pure (disorder free) ferromagnetic islands in the system. Excellent agreement is found by comparing this prediction to the experimental data on La0.7Ca0.3MnO3, from which I also extract the critical exponents. Next I report on studies of landscape formation due to carbonate precipitation near geothermal hot springs. This system forms complex patterns due to couplin