The Theory of Magnetism (Springer Series in Solid-state Sciences)

Science & Math

Daniel C. Mattis

Physics

Springer, Verlag

Starting with a historical introduction to the study of magnetism - one of the oldest sciences known to man - before considering the most modern theories and observations (magnetic bubbles and soap films, effects of magnetic impurities in metals and spin glasses), this book develops the concepts and the mathematical expertise necessary to understand contemporary research in this field. Magnetic systems are important in technology and applied science, but they are also prototypes of more complex mathematical structures of great importance to theoretical physics. These connections are made repeatedly in this volume. After development of the necessary quantum theory of angular momentum and of interacting electron systems, a number of models which have been successful in the interpretation of experimental results are introduced: the Ising model, the Heisenberg model, the Stoner theory, the Kondo phenomenon, and so on. In the second edition the thorough approach and the main features which made the first edition a popular text have been retained. All important theories are worked out in detail using methods and notation that are uniform throughout. Footnotes and an extensive bibliography provide a guide to the original literature. A number of problems test the reader's skill.

The Theory of Magnetism I: Statics and Dynamics (Springer Series in Solid-State Sciences)

Mathematics

Springer

What is thermodynamics? What does statistical physics teach us? In the pages of this slim book, we confront the answers. The reader will discover that where thermodynami cs provi des a 1 arge scal e, macroscopi c theory of the ef fects of temperature on physical systems, statistical mechanics provides the microscopic analysis of these effects which, invariably, are the results of thermal disorder. A number of systems in nature undergo dramatic changes in aspect and in their properties when subjected to changes in ambient temperature or pres sure, or when electric or magnetic fields are applied. The ancients already knew that a liquid, a solid, or a gas can represent different states of the same matter. But what is meant by "state"? It is here that the systematic study of magnetic materials has provided one of the best ways of examining this question, which is one of the principal concerns of statistical physics (alias "statistical mechanics") and of modern thermodynamics.

The Theory of Magnetism II: Thermodynamics and Statistical Mechanics (Springer Series in Solid-State Sciences)

Technology

The new edition of this text differs from the old in a number of ways. Classic discoveries which originally had to be omitted owing to lack of space - such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain - can now be incorporated. Many applications which did not even exist in 1966 (some of which were spawned by the first edition of this book) are newly included. Among these, the exact solution of the hubbard model, the notion of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, and a number of other contemporary concerns. Rather than bringing the topic of mathematical physics in one dimension completely up-to-date (self-evidently an impossible task) the authors have opted to complete the picture which they tentatively drew of this field, some 25 years ago in their first edition. This book is not aimed at all the new developments within this period which range from g-ology to string theory to two-dimensional gravity, etc., but has been designed as a most thorough exposition of a limited number of exactly soluble mathematical models of the many-body problem. As such it should serve as a guide and reference book to the classic early literature, while remaining accessible to graduate students and budding professionals in mathematics and theoretical physics. This volume should also provide a useful bridge to much of the current research literature in the topic.

Many-Body Problem, The: An Encyclopedia of Exactly Solved Models in One Dimension (3rd Printing with Revisions and Corrections)

World Scientific Publishing Company

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Books by Daniel C. Mattis