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Volume 1: From Brownian Motion to Renormalization and Lattice Gauge
Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal
Field Theory, and Random Systems. This two-volume work provides a
comprehensive and timely survey of the application of the methods
of quantum field theory to statistical physics, a very active and
fruitful area of modern research. The first volume provides a
pedagogical introduction to the subject, discussing Brownian
motion, its anticommutative counterpart in the guise of Onsager's
solution to the two-dimensional Ising model, the mean field or
Landau approximation, scaling ideas exemplified by the
Kosterlitz-Thouless theory for the XY transition, the continuous
renormalization group applied to the standard phi-to the fourth
theory (the simplest typical case) and lattice gauge theory as a
pathway to the understanding of quark confinement in quantum
chromodynamics. The second volume covers more diverse topics,
including strong coupling expansions and their analysis, Monte
Carlo simulations, two-dimensional conformal field theory, and
simple disordered systems. The book concludes with a chapter on
random geometry and the Polyakov model of random surfaces which
illustrates the relations between string theory and statistical
physics. The two volumes that make up this work will be useful to
theoretical physicists and applied mathematicians who are
interested in the exciting developments which have resulted from
the synthesis of field theory and statistical physics.
The second volume covers diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces, which illustrates the relations between string theory and statistical physics.
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