Statistical Field Theory: Volume 1, From Brownian Motion to Renormalization and Lattice Gauge Theory (Cambridge Monographs on Mathematical Physics)

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 theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics.

"I strongly recommend these two volumes to anyone from intermediate graduate students to active experienced researchers to aging veterans who need to be reminded of or learn for the first time the broad conceptual framework underlying the many current applications of field theoretic methods." Paul Ginsparg, Foundations of Physics

"...an excellent pedagogically oriented introduction to the essential fundamentals of this rapidly expanding field. The level of treatment and clarity make it suitable for use as a primary reference in a graduate course." D. J. Geldart, Physics in Canada