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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.

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Molecular dynamics simulations in three dimensions of particles that self-assemble to form two-dimensional, membrane-like objects are presented. Anisotropic, multibody forces, chosen so as to mimic real interactions between amphiphilic molecules, generate a finite rigidity and compressibility of the assembled membranes, as well as a finite line tension at their free edges. This model and its generalizations can be used to study a large class of phenomena taking place in fluctuating membranes. For instance, both fluid and solid-like phases, separated by a phase transition, are obtained and some of the large-scale properties of these membranes studied. In particular, thermal undulations of quasi-spherical fluid vesicles are analyzed, in a manner similar to recent experiments in lipid systems.

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