Application of combinatorial optimization algorithms in the study of elastic interfaces

A class of combinatorial optimization algorithms are applied in the study of disordered condensed matter systems. Two main classes of these systems, which include flux lines in high T c superconductors and domain walls in ferromagnetic systems, can be represented as interfaces subject to a time independent random potential. A variety of algorithms can be used to generate exact ground states of a these interfaces with the choice depending on the dimensionality and the correlations in the disorder potential. These simulations provide insights into the low temperature behavior of such condensed matter systems with impurities. Chapter 2 discusses the energy barriers encountered by a moving interface. It is proved that the motion of a discretized interface can be monotonic and still encounter the lowest possible energy barrier. The effectiveness of upper and lower bound algorithms that can be used to estimate the minimal energy barrier for the motion of a one dimensional interface is examined. In Chapter 3 a class of optimization algorithms which have been used to obtain ground state configurations in a range of statistical mechanics problems are presented. The results of the application of these algorithms in the study of the morphology of two dimensional interfaces are presented. Two types of loop representations can be derived from the minimal energy configurations of a two dimensional interface produced by these simulations. The properties of these loop models are analyzed and compared with the properties of loop models in the absence of disorder. Chapter 4 concentrates on the properties of three dimensional interfaces subject to a random potential which is periodic in one direction. Numerical simulation of ground states provides a clear picture of the structure and energetics of this system. In addition, the response of the system to changes in the external parameters is discussed