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The authors of “Series
Expansion Methods for Strongly Interacting Lattice Models”:
Chris Hamer, Jaan Oitmaa and Zheng Weihong |
Jaan Oitmaa, Chris Hamer and Zheng Weihong have
recently written a book entitled “Series Expansion Methods
for Strongly Interacting Lattice Models”. It is being published
by Cambridge University Press.
The book deals with methods for calculating high-order perturbation
series expansions for lattice models, and applications thereof.
We are among the world leaders in the development and use of these
powerful techniques. They can be used, for example, to explore the
behaviour of lattice models of quantum magnets, high-temperature
superconductors, and elementary particles, in situations where conventional
low-order approximations fail. In condensed matter physics the lattice
represents the underlying crystal lattice, as in the Heisenberg
model of magnetic materials, or the Hubbard model of conductors.
In lattice gauge theories, on the other hand, the lattice is merely
a mathematical artefact, useful for calculations in quantum chromodynamics.
Phase transitions and critical phenomena are one area of particular
interest. Here the interactions between the constituents are strong,
and long-range cooperative phenomena dominate the behaviour of the
system. High order series are essential to capture the behaviour
of the system.
Early chapters cover the classical treatment of critical phenomena
through high temperature expansions, and introduce graph theoretical
and combinatorial algorithms. The book then discusses high-order
linked-cluster perturbation expansions for quantum lattice models,
finite temperature expansions, and lattice gauge models. Numerous
detailed examples and case studies are included, and an accompanying
resources website contains programs for implementing these powerful
numerical techniques. We hope that the book will be a valuable resource
for graduate students and postdoctoral researchers working in condensed
matter and particle physics, and may also be useful as a reference
for specialized graduate courses on series expansion methods.
Jaan Oitmaa, Chris Hamer and Zheng Weihong
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