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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, weakly 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.
Topological defects formed at symmetry-breaking phase transitions play an important role in many different fields of physics. They appear in many condensed-matter systems at low temperature; examples include vortices in superfluid helium-4, a rich variety of defects in helium-3, quantized mag netic flux tubes in type-II superconductors, and disclination lines and other defects in liquid crystals. In cosmology, unified gauge theories of particle interactions suggest a sequence of phase transitions in the very early uni verse some of which may lead to defect formation. In astrophysics, defects play an important role in the dynamics of neutron stars. In 1997 the European Science Foundation started the scientific network "Topological defects" headed by Tom Kibble. This network has provided us with a unique opportunity of establishing a collaboration between the representatives of these very different branches of modern physics. The NATO-ASI (Advanced Study Institute), held in Les Houches in February 1999 thanks to the support of the Scientific Division of NATO, the European Science Foundation and the CNRS, represents a key event of this ESF network. It brought together participants from widely different fields, with diverse expertise and vocabulary, fostering the exchange of ideas. The lectures given by particle physicists, cosmologists and condensed matter physicists are the result of the fruitful collaborations established since 1997 between groups in several European countries and in the U.S.A.
This book treats the problem of phase transitions, emphasizing the generality and universality of the methods and models used. The course is basically concentrated on the problems of vacuum degeneration in macroscopic systems and a fundamental concept of quasiaverages by Bogolubov playing a special role in the theory of phase transitions and critical phenomena. An analysis of the connection between phase transition and spontaneous symmetry breaking in a macroscopic system allows a unique description of both first- and second-order phase transitions.The unique features of this book are:(i) a unique approach of describing first — as well as second-order phase transitions, based on the Bogolubov concept of quasi-averages.(ii) a detailed presentation of the material and at the same time a review of modern problems.(iii) a general character of developed ideas that could be applied to various particular systems of condensed matter physics, nuclear physics and high-energy physics.
About half a century ago Landau formulated the central principles of the phe nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.
Intended for readers with some prior knowledge of condensed-matter physics, this text emphasises the basic physics behind spontaneous structural changes in crystals. Starting with the relevant thermodynamic principles, the author discusses the nature of order variables and their collective motion in a crystal lattice. He also goes on to describe experimental methods for modulated crystal structures and gives examples of structural changes in representative systems. Both a graduate text and reference work.
"This book explains the thermodynamics and kinetics of most of the important phase transitions in materials science. It is a textbook, so the emphasis is on explanations of phenomena rather than a scholarly assessment of their origins. The goal is explanations that are concise, clear, and reasonably complete. The level and detail are appropriate for upper division undergraduate students and graduate students in materials science andmaterials physics. The book should also be useful for researchers who are not specialists in these fields. The book is organized for approximately sequential coverage in a graduate-level course. The four parts of the book serve different purposes, however, and should be approached differently"--
Quantum phase transitions (QPTs) offer wonderful examples of the radical macroscopic effects inherent in quantum physics: phase changes between different forms of matter driven by quantum rather than thermal fluctuations, typically at very low temperatures. QPTs provide new insight into outstanding problems such as high-temperature superconductivit
Quantum Phase Transitions is the first book to describe in detail the fundamental changes that can occur in the macroscopic nature of matter at zero temperature due to small variations in a given external parameter. The subject plays a central role in the study of the electrical and magnetic properties of numerous important solid state materials. The author begins by developing the theory of quantum phase transitions in the simplest possible class of non-disordered, interacting systems - the quantum Ising and rotor models. Particular attention is paid to their non-zero temperature dynamic and transport properties in the vicinity of the quantum critical point. Several other quantum phase transitions of increasing complexity are then discussed and clarified. Throughout, the author interweaves experimental results with presentation of theoretical models, and well over 500 references are included. The book will be of great interest to graduate students and researchers in condensed matter physics.
"The research described in this thesis focuses on topological phases in condensed matter systems. It can be roughly divided into two parts. In the first part noninteracting systems are studied. The symmetry algebra of a charged spin-1/2 particle coupled to a non-Abelian magnetic field is determined, which explains the finite and infinite degeneracy of the energy. This system is a candidate for a continuum model of a three-dimensional topological insulator. Next, a two-dimensional version is considered on a sphere, where its spectrum is solved. The planar version of the sam model is probed by the insertion of a non-Abelian flux. Starting from a spin-polarized state, the adiabatic insertion of the flux results in a state with nontrivial spin-texture which is recognized as a quantum Hall skyrmion. The second part covers topological phases which stem from an underlying interacting model and that carry quasiparticles with fractional statistics. By applying a technique called topological symmetry breaking transitions between different phases can be induced. A careful treatment shows that different domains may appear in the broken phase separated by domain walls and it leads to a clear interpretation of confined particles. Moreover, phase transitions induced by multilayered condensates are considered. Non-Abelian phases as well as an entire hierarchy of Abelian fractional quantum Hall states are treated. A special focus is given to the study of the one-dimensional boundary between the two phases."--Samenvatting auteur.
This volume comprises the proceedings of a NATO Advanced Study Institute held in Geilo, Norway, between 4 - 14 April 1989. This Institute was the tenth in a series held at Geilo on the subject of phase transitions. It was the first to be concerned with the growing area of soft condensed matter, which is neither ordinary solids nor ordinary liquids, but somewhere in between. The Institute brought together many lecturers, students and active researchers in the field from a wide range of NATO and some non-NATO countries, with financial support principally from the NATO Scientific Affairs Division but also from Institutt for energiteknikk, the Nor wegian Research Council for Science and the Humanities (NAVF), The Nordic Institute for Theoretical Atomic Physics (NORDITA), the Norwegian Physical Society and VISTA, a reserach cooperation between the Norwegian Academy of Science and Letters and Den norske stats oljeselskap a.s (STATOIL). The organizing committee would like to thank all these contributors for their help in promoting an exciting and rewarding meeting, and in doing so are confident that they echo the appreciation also of all the participants. 50ft condensed matter is characterized by weak interactions between polyatomic constituents, by important·thermal fluctuations effects, by mechanical softness and by a rich range of behaviours. The main emphasis at this Institute was on the fundamental collective physics, but prepar ation techniques and industrial applications were also considered.