The Occurrence and Nature of Modulated Structures in One-Dimensional Models with Nonconvex Neighbour Interactions

In this work we present an in depth analysis of the ground state properties of one-dimensional models of classical particles in a periodic substrate potential, V, and with nonconvex nearest neighbour interactions, W. Using the method of effective potentials we are able to construct phase diagrams for these models. A detailed study is presented for particular models where V is convex and where W has either a Lennard-Jones -like or a double-well form. In both cases, many of the interesting features found in the ground state diagram can be understood with the help of an analytic model where W is constructed piecewise linearly. In this way the dependence of the order of phase transitions on the convexity of W and the presence of superdegenerate points are explained. We also study a different system consisting of two chains of particles coupled in a ladder configuration. We show that this model can be transformed into a single chain model similar to those described above with a periodic substrate potential and with nearest neighbour interactions. The variation of a linear density in the double chain with movement in parameter space and its relevance to experimentally observable results is discussed.