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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Phase transitions in simple systems
Mean field theory
The renormalization group idea
Phase diagrams and fixed points
The perturbative renormalization group
Low dimensional systems
Surface critical behaviour
argument block spin boundary conditions bulk calculation coefficient configuration conformal transformation consider correlation function correlation length corresponding coupling critical behaviour critical exponents critical fixed point critical point critical temperature cross-over defined degrees of freedom depends described dimensional dynamics eigenvalue energy density example expect fact factor ferromagnet finite fluctuations free energy Gaussian fixed point Gaussian model generalisation given hamiltonian integral interaction invariant irrelevant Ising model lattice limit linear low temperature magnetic field magnetisation mean field theory operator product expansion order parameter partition function percolation perturbative phase diagram phase transition physical polymer Potts model problem quantities quantum random field relevant renormalization group eigenvalue renormalization group equation renormalization group flows rescaling result right hand side scaling dimension scaling form scaling operators scaling variable Section simple singular specific heat symmetry thermodynamic tion trajectory tricritical point two-point universality class upper critical dimension vanish vortices XY model