Scaling and Renormalization in Statistical PhysicsCambridge 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. |
Inhalt
4 | 24 |
1 | 30 |
4 | 43 |
8 | 52 |
4 | 60 |
3 | 67 |
5 | 76 |
The perturbative renormalization group | 83 |
Surface critical behaviour | 133 |
71 | 140 |
Random systems | 145 |
Polymer statistics | 169 |
Critical dynamics | 183 |
Conformal symmetry | 206 |
Gaussian integration | 227 |
234 | |
Häufige Begriffe und Wortgruppen
argument block spin boundary conditions bulk calculation coefficient configuration consider continuous spin 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 distance dynamics e-expansion eigenvalue energy density example expect fact factor ferromagnet Figure 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 mean field theory non-trivial fixed point non-zero operator product expansion order parameter partition function percolation phase diagram phase transition physical polymer Potts model problem quantities quantum r₁ random field relevant renormalization group eigenvalue renormalization group equation renormalization group flows rescaling result right hand side scaling dimension scaling operators scaling variables Section simple singular specific heat surface symmetry tion tricritical universality class upper critical dimension vanish vortices XY model