Theory Of Symmetry Changes At Continuous Phase Transitions

The contents of this book stems from three different objectives. First, it is an introduction to the basic principles and techniques of Landau's theory, which is intended for teaching purposes. A second purpose of the book provides the practical methods for applying Landau's theory to complex systems. The last objective of the book is to incorporate the developments which have arisen in the last fifteen years from the extensive application of the theory to a variety of physical systems.

Theory of Phase Transitions: Rigorous Results is inspired by lectures on mathematical problems of statistical physics presented in the Mathematical Institute of the Hungarian Academy of Sciences, Budapest. The aim of the book is to expound a series of rigorous results about the theory of phase transitions. The book consists of four chapters, wherein the first chapter discusses the Hamiltonian, its symmetry group, and the limit Gibbs distributions corresponding to a given Hamiltonian. The second chapter studies the phase diagrams of lattice models that are considered at low temperatures. The notions of a ground state of a Hamiltonian and the stability of the set of the ground states of a Hamiltonian are also introduced. Chapter 3 presents the basic theorems about lattice models with continuous symmetry, and Chapter 4 focuses on the second-order phase transitions and on the theory of scaling probability distributions, connected to these phase transitions. Specialists in statistical physics and other related fields will greatly benefit from this publication.

Symmetry 2 aims to present an overview of the contemporary status of symmetry studies, particularly in the arts and sciences, emphasizing both its role and importance. Symmetry is not only one of the fundamental concepts in science, but is also possibly the best unifying concept between various branches of science, the arts and other human activities. Whereas symmetry has been considered important for centuries primarily for its aesthetic appeal, this century has witnessed a dramatic enhancement of its status as a cornerstone in the sciences. In addition to traditionally symmetry-oriented fields such as crystallography and spectroscopy, the concept has made headway in fields as varied as reaction chemistry, nuclear physics, and the study of the origin of the universe. The book was initiated in response to the success of the first volume, which not only received good reviews, but received the award for "The Best Single Issue of a Journal" by the Association of American Publishers for 1986. The second volume extends the application of symmetry to new fields, such as medical sciences and economics, as well as investigating further certain topics introduced in Symmetry. The book is extensively illustrated and with over 64 contributions from 16 countries presents an international overview of the nature and diversity of symmetry studies today.

In this volume new group-theoretical methods for investigating phase transitions and symmetry problems in various types of crystals and liquid crystals are presented. New topics pertaining to the area of application of the theories of Landau and Birman, such as, transitions to modulated structures and the description of their symmetry, are discussed. Examples of applications of the group-theoretical methods are given, containing detailed calculations of symmetry changes at structural, magnetic, improper ferroelectric, commensurate-to-incommensurate, field-induced metamagnetic and liquid crystal phase transitions. This book will be invaluable to research workers at universities and scientific laboratories and postgraduate students specializing in solid state theory.

Advanced Structural Chemistry Discover the relationships between inorganic chemical synthesis, structure, and property with these comprehensive and insightful volumes Advanced Structural Chemistry: Tailoring Properties of Inorganic Materials and their Applications (3 Volume Set) offers readers the opportunity to discover the relationship between the structure and function of matter, develop efficient and precise synthesis methodology, and to understand the theoretical tools for new functional substances. Advanced Structural Chemistry clarifies the relationships between synthesis and structure, as well as structure and property, both of which are central to the creation of new materials with unique functions. In addition to subjects like the syntheses of metal-oxide clusters, metal-organic cages, and metal-organic frameworks with tailored optical, electric, ferroelectric, magnetic, adsorption, separation, and catalytic properties, the accomplished editor Rong Cao provides readers with information on a wide variety of topics, such as: Coordination-assembled metal-organic macrocycles and cages, including metallacycles and metallacages The structural chemistry of metal-oxo clusters, including the oxo clusters of transition metal, main group metal, and lanthanides Synthetic approaches, structural diversities, and biological aspects of molybdenum-based heterometallic sulfide clusters and coordination polymers Group 11-15 metal chalcogenides, including discrete chalcogenide clusters synthesized in ionic liquids The structures of metal-organic frameworks, including one-, two-, and three-dimensional MOFs Perfect for inorganic chemists, structural chemists, solid state chemists, material scientists, and solid state physicists, Advanced Structural Chemistry also belongs on the bookshelves of catalytic and industrial chemists who seek to improve their understanding of the structure and functions of inorganic materials.

Unlike existing texts, this book blends for the first time three topics in physics - symmetry, condensed matter physics and computational methods - into one pedagogical textbook. It includes new concepts in mathematical crystallography; experimental methods capitalizing on symmetry aspects; non-conventional applications such as Fourier crystallography, color groups, quasicrystals and incommensurate systems; as well as concepts and techniques behind the Landau theory of phase transitions. Adopting a computational approach to the application of group theoretical techniques to solving symmetry related problems, it dramatically alleviates the need for intensive calculations usually found in the presentation of symmetry. Writing computer programs helps the student achieve a firm understanding of the underlying concepts, and sample programs, based on Mathematica, are presented throughout the book. Containing over 150 exercises, this textbook is ideal for graduate students in condensed matter physics, materials science, and chemistry. Solutions and computer programs are available online at www.cambridge.org/9780521828451.