Efficient calculation of complex multidimensional phase diagrams of discrete-lattice models Original Research Article

Among the tasks encountered in the treatment of models from various scientific disciplines is the classification of particular values of adjustable parameters according to the respective types of structures predicted by the model. This problem is analogous to the determination of phase diagrams used in condensed-matter theory. We focus on discrete-lattice models for modulated materials which give rise to complex phase diagrams due to the occurrence of long-period and near-degenerate modulated structures. Algorithms are presented which can in some cases replace less efficient traditional methods for the calculation of phase diagrams. They exploit topological features of the phase diagrams and — in the case of microscopic models — symmetries in the spatial variation of the model variables, provided that prior knowledge from other methods is at hand.