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In a comprehensive treatment of Statistical Mechanics from
thermodynamics through the renormalization group, this book serves
as the core text for a full-year graduate course in statistical
mechanics at either the Masters or Ph.D. level. Each chapter
contains numerous exercises, and several chapters treat special
topics which can be used as the basis for student projects. The
concept of scaling is introduced early and used extensively
throughout the text. At the heart of the book is an extensive
treatment of mean field theory, from the simplest decoupling
approach, through the density matrix formalism, to self-consistent
classical and quantum field theory as well as exact solutions on
the Cayley tree. Proceeding beyond mean field theory, the book
discusses exact mappings involving Potts models, percolation,
self-avoiding walks and quenched randomness, connecting various
athermal and thermal models. Computational methods such as series
expansions and Monte Carlo simulations are discussed, along with
exact solutions to the 1D quantum and 2D classical Ising models.
The renormalization group formalism is developed, starting from
real-space RG and proceeding through a detailed treatment of
Wilson's epsilon expansion. Finally the subject of
Kosterlitz-Thouless systems is introduced from a historical
perspective and then treated by methods due to Anderson,
Kosterlitz, Thouless and Young. Altogether, this comprehensive,
up-to-date, and engaging text offers an ideal package for advanced
undergraduate or graduate courses or for use in self study.
In a comprehensive treatment of Statistical Mechanics from
thermodynamics through the renormalization group, this book serves
as the core text for a full-year graduate course in statistical
mechanics at either the Masters or Ph.D. level. Each chapter
contains numerous exercises, and several chapters treat special
topics which can be used as the basis for student projects. The
concept of scaling is introduced early and used extensively
throughout the text. At the heart of the book is an extensive
treatment of mean field theory, from the simplest decoupling
approach, through the density matrix formalism, to self-consistent
classical and quantum field theory as well as exact solutions on
the Cayley tree. Proceeding beyond mean field theory, the book
discusses exact mappings involving Potts models, percolation,
self-avoiding walks and quenched randomness, connecting various
athermal and thermal models. Computational methods such as series
expansions and Monte Carlo simulations are discussed, along with
exact solutions to the 1D quantum and 2D classical Ising models.
The renormalization group formalism is developed, starting from
real-space RG and proceeding through a detailed treatment of
Wilson's epsilon expansion. Finally the subject of
Kosterlitz-Thouless systems is introduced from a historical
perspective and then treated by methods due to Anderson,
Kosterlitz, Thouless and Young. Altogether, this comprehensive,
up-to-date, and engaging text offers an ideal package for advanced
undergraduate or graduate courses or for use in self study.
Engineers and technologists often operate from a worldview of 'ones
and zeros.' The mission of this book is to interject the colorful
world of creative thinking to help engineers and technologists
learn to think and work differently. Thus, 'idea engineering'
becomes the driving force, transforming engineers and technologists
into innovators and entrepreneurs, using case studies and anecdotes
from first-hand experience. The material in this book is organized
to take the reader through basic concepts and techniques of
creative thinking and innovation, to better solve engineering and
technological challenges. It provides an overall understanding of
who, what, why, when, and how 'idea engineering' can transform an
individual and a company to formulate and apply the best
possibilities.
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