The Theory of Magnetism Made Simple: An Introduction to Physical Concepts and to Some Useful Mathematical Methods
The original edition of The Theory of Magnetism was the first book to develop the various relevant topics using modern methods adapted for the many-body problem and thus it became popular (reportedly the "most-stolen" book from the exhibition stalls at the March meeting of the American Physical Society!). It presented and taught the fermionic field theory central to Onsager's analysis of the statistical mechanics of the two-dimensional Ising model of magnetism. In its pages the Lieb-Mattis theorems on magnetic ordering of electronic energy levels and on the absence of ferromagnetism in one dimension were restated and proved in a form accessible to students. The exchange mechanism in insulators and the Ruderman-Kittel interaction in metals were some of the innovative topics presented to the reader. Spin waves and their interactions were analyzed in some detail. The first chapter, on the history of physics as seen through the prism of research in magnetism, co-authored with Dr Noemi Mattis, proved especially popular. In this new edition, while retaining much of the material in earlier editions, especially the first chapter, the author has eliminated some of the bulk (the most recent edition was in two volumes) and added a number of new subjects. Among these are the effects of lowering the dimensionality (exact solutions of some important models in zero and one dimension are exhibited and contrasted with the three-dimensional versions) and the importance of the two-body Coulomb interactions. The reader is introduced to the topic of critical exponents, which has been so marvellously worked out in recent decades. Quoting a novel theorem by Lieb and exotic band structures, the authorre-examines the origins of ferromagnetism. In the presentation, physical principles come first, the mathematics second. Developing the reader's intuition and mastery of the subject takes precedence. Because of this the book was not
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Quantum Theory of Angular Momentum
Magnetism and the ManyBody Problem
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angular momentum anticommutation antiferromagnet antiparallel approximation arbitrary atomic band bonds bound boundary conditions calculation classical commute configurations constant correlation functions Coulomb critical critical exponents Curie temperature defined denoted density derived diagonal dimensions effect eigenfunctions eigenstates eigenvalue electrons elementary excitations equation evaluate example exchange external field factor Fermi fermions ferromagnetic finite formula free energy given ground state energy Hamiltonian Heisenberg Hubbard model Hund's rule impurity integral interactions Ising model Kondo lattice Lett limit linear long-range magnetic field magnitude magnon matrix elements metals nearest-neighbor neighbors nonmagnetic obtain operators paramagnetic parameter particles partition function Pauli phase transition Phys physics plane Problem properties quantized quantum numbers random shell singlet sinh solution solved specific heat spectrum spherical model spin glass sublattice susceptibility symmetry temperature theorem thermal thermodynamic tion total spin transfer matrix transformation vanishes vector XY model yields zero