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Focusing on the purely theoretical aspects of strongly correlated electrons, this volume brings together a variety of approaches to models of the Hubbard type – i.e., problems where both localized and delocalized elements are present in low dimensions. The chapters are arranged in three parts. The first part deals with two of the most widely used numerical methods in strongly correlated electrons, the density matrix renormalization group and the quantum Monte Carlo method. The second part covers Lagrangian, Functional Integral, Renormalization Group, Conformal, and Bosonization methods that can be applied to one-dimensional or weakly coupled chains. The third part considers functional derivatives, mean-field, self-consistent methods, slave-bosons, and extensions. Taken together, the contributions to this volume represent a comprehensive overview of current problems and developments.
This invaluable book is a collection of lectures delivered at the Colloquium 'Mathematical Results in Statistical Mechanics' held in Marseilles, France, on July 27-31, 1998, as a satellite colloquium of the Paris conference STATPHYS 20. It covers a large part of the contemporary results in statistical mechanics, from the point of view of mathematical physics, by leading experts in this field. It includes as the main topics, phase transitions, interfaces, disordered systems, Gibbsian and non-Gibbsian states, as well as recent rigorous treatments in quantum statistical mechanics.
Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.
The volume presents, for the very first time, an exhaustive collection of those modern theoretical methods specifically tailored for the analysis of Strongly Correlated Systems. Many novel materials, with functional properties emerging from macroscopic quantum behaviors at the frontier of modern research in physics, chemistry and materials science, belong to this class of systems. Any technique is presented in great detail by its own inventor or by one of the world-wide recognized main contributors. The exposition has a clear pedagogical cut and fully reports on the most relevant case study where the specific technique showed to be very successful in describing and enlightening the puzzling physics of a particular strongly correlated system. The book is intended for advanced graduate students and post-docs in the field as textbook and/or main reference, but also for other researchers in the field who appreciates consulting a single, but comprehensive, source or wishes to get acquainted, in a as painless as possible way, with the working details of a specific technique.
Cet ouvrage est une réédition numérique d’un livre paru au XXe siècle, désormais indisponible dans son format d’origine.
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First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.