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

This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once 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, or Bethe's original paper on the Bethe ansatz -- can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.

"This volume is a thoroughly extended and updated version of the classic Mathematical physics in one dimension, by Lieb and Mattis ... In short, this encyclopedic compendium will be of value to many researchers working in 'exact results'." Mathematical Reviews