Scaling in Condensed Matter Physics: the Kondo Problem, Aggregation, and the RandomField Ising Model.
Abstract
Scaling concepts are applied to three problems in condensed matter physics. The N orbital, single impurity Kondo problem is shown to be equivalent to an N state Potts model in one dimension with inversesquare interactions. Using renormalization techniques, it is found that the peak in the static magnetic susceptibility at finite N develops into a discontinuity as Ntoinfty. A scaling hypothesis is consistent with an increase in the peak height as ln N. The practice of using a high energy cutoff such as the bandwidth as an effective temperature is discussed. Secondly, a generalized model of aggregation is introduced in which particles interact at a distance. For infiniterange interactions, the model is solved exactly. A scaling ansatz, similar to that made in finitesize scaling of critical phenomena, is used to extrapolate the results to finite range. Computer simulations support this ansatz. Lastly, the twodimensional randomfield Ising model is used to model monolayer adsorption onto a substrate with quenched, random impurities. From renormalization group arguments, we obtain expressions for the zerofield susceptibility as a function of the linear dimension of a typical crystallite and the width of the field distribution. The Curielaw divergence of the susceptibility found at low temperatures for pure finitesized crystallites is removed in the presence of impurities.
 Publication:

Ph.D. Thesis
 Pub Date:
 1987
 Bibcode:
 1987PhDT........66G
 Keywords:

 Physics: Condensed Matter