A review of Statistical Field Theory. Volume 1. From Brownian Motion to Renormalization and Lattice Gauge Theory, and Statistical Field Theory. Volume 2. Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems. By Claude Itzykson and Jean-Michel Drouffe. Volume 1 (Cambridge University Press, 1989.) [Pp. xvi + 4031 £25.00. ISBN 0 521 34058 6. Volume 2. (Cambridge University Press, 1989.) [Pp. xvi + 4051 £25.00. ISBN 0 521 37012 4.
A review of Statistical Field Theory. Volume 1. From Brownian Motion to Renormalization and Lattice Gauge Theory, and Statistical Field Theory. Volume 2. Strong Coupling, Monte Carlo Methods, Conformal Field Theory and Random Systems. By Claude Itzykson and Jean-Michel Drouffe. Volume 1 (Cambridge University Press, 1989.) [Pp. xvi + 4031 £25.00. ISBN 0 521 34058 6. Volume 2. (Cambridge University Press, 1989.) [Pp. xvi + 4051 £25.00. ISBN 0 521 37012 4.
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.
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.
General principles of statistical mechanics, P.A. Pearce the connection between statistical mechanics and quantum field theory, B.M. McCoy two-dimensional models in statistical mechanics, R.J. Baxter topics in conformal field theory, C. Itzykson quantum gravity as dynamical triangulation, A.A. Migdal lattice gauge theory, C.J. Hamer quantum groups for physicists, M. Gould chaos versus order in Hamiltonian dynamical systems, G.R.W. Quispel quantum and classical integrable systems and statistical mechanics, R.K. Bullough and J.T. Timonen introduction to quantum field theory, R.J. Crewther.
(in French) G Toulouse and P Pfeuty Grenoble: Presses Universitaires de Grenoble 1975 pp 278 price FF 65 Of all the important developments in theoretical physics over the last 20 years or more, the recent burgeoning of the renormalization group in statistical mechanics and in field theory has surely been the least well served by general reviews and introductions. Though exciting in their overall tenour and useful to the already active researcher, these have been exceptionally difficult of access even from immediately neighbouring fields.