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The aim of this book is to provide the fundamentals of statistical
physics and its application to condensed matter. The combination of
statistical mechanics and quantum mechanics has provided an
understanding of properties of matter leading to spectacular
technological innovations and discoveries in condensed matter which
have radically changed our daily life.The book gives the steps to
follow to understand fundamental theories and to apply these to
real materials.
The aim of this book is to provide the fundamentals of statistical
physics and its application to condensed matter. The combination of
statistical mechanics and quantum mechanics has provided an
understanding of properties of matter leading to spectacular
technological innovations and discoveries in condensed matter which
have radically changed our daily life.The book gives the steps to
follow to understand fundamental theories and to apply these to
real materials.
The book is intended for graduate students and researchers who wish
to master the main properties of magnetic materials in the bulk
state and at the nanometric scale such as for thin films and
multilayers. This textbook provides the theories and methods of
simulation to study and to understand these properties in an
explicit manner.In the first part of the book, the quantum theory
of magnetism is presented while the second part of the book is
devoted to the application of the theory of magnetism to surface
physics. Numerous examples covering typical cases in ferromagnets,
antiferromagnets, ferrimagnets, helimagnets, and frustrated spin
systems are all illustrated. Fundamental surface effects are shown
and discussed. Lastly, the spin transport is described - in which
the basic formulation of the Boltzmann's equation is recalled - and
the recent methods of Monte Carlo simulation to deal with the spin
resistivity are explained.This book contains a large number of
detailed solutions for the problems given in each chapter to help
readers discover new related phenomena and applications, as well as
an appendix on elements of statistical physics included at the end
to make the book self-contained.
This book covers all principal aspects of currently investigated
frustrated systems, from exactly solved frustrated models to real
experimental frustrated systems, going through renormalization
group treatment, Monte Carlo investigation of frustrated classical
Ising and vector spin models, low-dimensional systems, spin ice and
quantum spin glass. The reader can - within a single book - obtain
a global view of the current research development in the field of
frustrated systems.This new edition is updated with recent
theoretical, numerical and experimental developments in the field
of frustrated spin systems. The first edition of the book appeared
in 2005. In this edition, more recent works until 2012 are
reviewed. It contains nine chapters written by researchers who have
actively contributed to the field. Many results are from recent
works of the authors.The book is intended for postgraduate students
as well as researchers in statistical physics, magnetism, materials
science and various domains where real systems can be described
with the spin language. Explicit demonstrations of formulas and
full arguments leading to important results are given where it is
possible to do so.
Frustrated spin systems have been first investigated five decades
ago. Well-known examples include the Ising model on the
antiferromagnetic triangular lattice studied by G H Wannier in 1950
and the Heisenberg helical structure discovered independently by A
Yoshimori, J Villainn and T A Kaplan in 1959. However, extensive
investigations on frustrated spin systems have really started with
the concept of frustration introduced at the same time by G
Toulouse and by J Villain in 1977 in the context of spin glasses.
The frustration is generated by the competition of different kinds
of interaction and/or by the lattice geometry. As a result, in the
ground state all bonds are not fully satisfied. In frustrated Ising
spin systems, a number of spins behave as free spins. In frustrated
vector spin systems, the ground-state configuration is usually
non-collinear. The ground state of frustrated spin systems is
therefore highly degenerate and new induced symmetries give rise to
unexpected behaviors at finite temperatures. Many properties of
frustrated systems are still not well understood at present.
Theoretically, recent studies shown in this book reveal that
established theories, numerical simulations as well as experimental
techniques have encountered many difficulties in dealing with
frustrated systems. In some sense, frustrated systems provide an
excellent testing ground for approximations and theories.
Experimentally, more and more frustrated materials are discovered
with interesting properties for applications.
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