| We present our findings on four topics relating to disordered spin systems. The first is on a technique to optimize Monte Carlo simulations. This technique was successfully applied to simple models, such as the Ising ferromagnet, in earlier published work. We explore its application to a basic spin glass model and find it of limited use. Put simply, spin glasses are too different qualitatively from the systems for which the optimization was shown to be effective.;The second topic concerns the debate over the existence of the Almeida-Thouless (AT) line i.e. whether or not Ising spin glasses have a transition in a field. We study an Ising spin glass on a one-dimensional model which has interactions that decay as a power of distance; tuning this power allows us to modify the effective range of the system. The analysis is based on a finite-size scaling of the dimensionless correlation length, which we use to find evidence for second-order transitions. Our results suggest that an AT line exists for dimensions greater than six and does not exist for lower dimensions. The data shown are from simulations by Katzgraber, while Larson checked select results with independent source code to ensure their validity. All collaborators contributed to the analysis of these data.;Third, we investigate a "p-spin" spin glass, for p = 3, motivated by analogies to structural glass physics as well as an argument that it belongs in the same universality class as the Ising model in a field. Specifically, there is a strong connection between the mean field dynamics of this model and the Mode Coupling Theory of structural glasses. The goal is to see if the mean field description carries to low dimensionality. We use a similar one-dimensional model to the above in order to probe multiple dimensions for phase transitions. We again look for evidence in the correlation length. The findings indicate transitions both above and below a dimension of six, though the transition disappears for sufficiently low dimension (above dl). We discuss possible sources for the different behavior between the 3-spin model and the Ising glass in a field.;In the last topic we look for evidence of the Griffiths singularity in a bond-diluted two-dimensional XY ferromagnet. The Griffiths singularity should appear (weakly) in the tail of the susceptibility distribution for different bond realizations. We apply a powerful distribution-sampling technique to this end. Our results suggest that the susceptibility distribution does indeed respond to the singularity, though not as cleanly as in a similar study on the Ising model. The weaker form of ordering for XY models may be the cause of this. |
