Abstract
Abstract We study a one-dimensional lattice model with an on-site double-quadratic potential, where first- and second-neighbour interactions are taken into account. We investigate commensurate states of the model and we study in detail the interactions between domain walls as a function of the spatial distribution of those walls within two and four-wall structures. We then find the spatial distribution of the walls which corresponds to the lowest energy of the structure and identify the unit cells associated with the ground states. We then suggest a method incorporating domain-wall interactions to build up the phase diagram of the model using a two-step process: first, we determine by the above process the ground states of the model in the parameter space that is considered. Second, we determine classically the parameter regions corresponding to each ground state.
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