This book provides an introduction to conformal field theory and a review of its applications to critical phenomena in condensed-matter systems. After reviewing simple phase transitions and explaining the foundations of conformal invariance and the algebraic methods required, it proceeds to the explicit calculation of four-point correlators. Numerical methods for matrix diagonalization are described as well as finite-size scaling techniques and their conformal extensions. Many exercises are included. Applications treat the Ising, Potts, chiral Potts, Yang-Lee, percolation and XY models, the XXZ chain, linear polymers, tricritical points, conformal turbulence, surface criticality and profiles, defect lines and aperiodically modulated systems, persistent currents and dynamical scaling. The vicinity of the critical point is studied culminating in the exact solution of the two-dimensional Ising model at the critical temperature in a magnetic field. Relevant experimental results are also reviewed.
Critical Phenomena: A Reminder.- Conformal Invariance.- Finite Size Scaling.- Representation Theory of the Virasoro Algebra.- Correlators, Null Vectors and Operator Algebra.- Ising Model Correlators.- Coulomb Gas Realization.- The Hamiltonian Limit and Universality.- Numerical Techniques.-Conformal Invariance in the Ising Quantum Chain.- Modular Invariance.- Further Developments and Applications.- Conformal Perturbation Theory.- The Vicinity of the Critical Point.- Surface Critical Phenomena.- Strongly Anisotropic Scaling.
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