Scaling and Renormalization in Statistical Physics
Cambridge University Press, 26.04.1996 - 238 Seiten
This text provides a thoroughly modern graduate-level introduction to the theory of critical behavior. Beginning with a brief review of phase transitions in simple systems and of mean field theory, the text then goes on to introduce the core ideas of the renormalization group. Following chapters cover phase diagrams, fixed points, cross-over behavior, finite-size scaling, perturbative renormalization methods, low-dimensional systems, surface critical behavior, random systems, percolation, polymer statistics, critical dynamics and conformal symmetry. The book closes with an appendix on Gaussian integration, a selected bibliography, and a detailed index. Many problems are included. The emphasis throughout is on providing an elementary and intuitive approach. In particular, the perturbative method introduced leads, among applications, to a simple derivation of the epsilon expansion in which all the actual calculations (at least to lowest order) reduce to simple counting, avoiding the need for Feynman diagrams.
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analysis approach approximation argument block boundary bulk calculation called close coefficient conformal connected consider constant continuous corrections correlation function correlation length corresponding coupling critical behaviour critical point defined degrees of freedom density depends derivatives described diagram dimensions direction discussed distance dynamics effective eigenvalue equation example expect exponents fact factor Figure finite fixed point flows fluctuations follows free energy Gaussian given gives hamiltonian hand side important integral interaction invariant irrelevant Ising model lattice leading limit magnetic magnetisation Note operator operator product expansion original parameter perturbative phase physical possible powers problem properties proportional quantities quantum random reduced region relevant renormalization group renormalization group equation rescaling respect result scaling scaling dimension shown simple singular space spin sufficiently Suppose surface symmetry temperature term tion transformation transition usual vanish variable write zero