Ground state domain patterns in modulated systems

Abstract

A lot of systems display domain patterns at equilibrium. Some commonly observed patterns are bubbles and stripes in two-dimensional systems; or droplets, tubes and sheets in three-dimensional systems. In this thesis, the 2D patterns are studied by an energetic approach, using the Ising model with generalized interactions as the model. Several concepts in statistical physics, such as Legendre transformation and the correlation function, are proved to be helpful in the understanding of the behavior of the model. One important implication is that a power-law interaction may be approximated as a simple short-range interaction plus a chemical potential. These concepts also help in developing a simple and efficient method in prediction of the ground state. Another focus of this thesis is to investigate the assumptions made in the method. Our method first assumes some structures like bubbles and stripes, but complex patterns are sometimes possible. We identify that the preference of particle separation is the product of two factors, namely, the particle density and an interaction-dependent term. Complex patterns can be understood as the result of competitions between two factors of the preference and the qualitative features of such interactions are discussed. Finally, a proof of ground state periodicity is given using Fourier series.

Date of Award	2017
Original language	English
Awarding Institution	The Hong Kong University of Science and Technology