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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, is provided in two volumes. 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...

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.

Quantum field theory remains among the most important tools in defining and explaining the microscopic world. Recent years have witnessed a blossoming of developments and applications that extend far beyond the theory's original scope. This comprehensive text offers a balanced treatment, providing students with both a formal presentation and numerous practical examples of calculations.
This two-part approach begins with the standard quantization of electrodynamics, culminating in the perturbative renormalization. The second part comprises functional methods, relativistic bound states,...