Discontinuous (first-order) phase transitions constitute the most fundamental and widespread type of structural transitions existing in Nature, forming a large majority of the transitions found in elemental crystals, alloys, inorganic compounds, minerals and complex fluids. Nevertheless, only a small part of them, namely, weekly discontinuous transformations, were considered by phenomenological theories, leaving aside the most interesting from a theoretical point of view and the most important for application cases. Discontinuous Phase Transitions in Condensed Matter introduces a density-wave approach to phase transitions which results in a unified, symmetry-based, model-free theory of the weak crystallization of molecular mixtures to liquid-crystalline mesophases, strongly discontinuous crystallization from molten metals and alloys to conventional, fully segregated crystals, to aperiodic, quasi-crystalline structures. Assembly of aperiodic closed virus capsids with non-crystallographic symmetry also falls into the domain of applicability of the density-wave approach.The book also considers the applicability domains of the symmetry-based approach in physics of low-dimensional systems. It includes comparisons of stability of different surface superstructures and metal monoatomic coverage structures on the surface of single-crystalline substrates. The example of the twisted graphene bilayer demonstrates how parametrization in the spirit of an advanced phenomenological approach can establish symmetry-controlled, and therefore model-free, links between geometrical parameters of the twisted bilayer structure and reconstruction of its Brillouin zone and energy bands.Key FeaturesDespite a long history and considerable progress in the field, no new titles have recently appeared on the corresponding topic of this titleImportantly, this book will be the first publication which presents the current status of the phenomenological theory of phase transitions in its entire but compact form, making this a unique textbook on the subjectThe book will prove helpful to a wide audience of students, researchers, and lecturing professorsThe book offers not only new domains of applicability (such as martensitic transformations, crystallization of the crystalline and aperiodic bulk materials, complex fluids or viruses) where the theory demonstrates its efficiency, but it also equips the investigator with the necessary methods and theoretical tools to control and manage their experiments

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