A MODERN APPROACH TO CRITICAL PHENOMENA

By J. MITIE

CONTENTS INTRODUCTION 1 1 PHASE TRANSITIONS AND ORDER PARAMETERS 1 2 MODELS: ISING, XY, HEISENBERG 1 3 UNIVERSALITY AND CRITICAL EXPONENTS 1 4 SCALING OF FREE ENERGY 1 5 CORRELATIONS AND HYPERSCALING GINZBURG–LANDAU–WILSON THEORY 2 1 PARTITION FUNCTION FOR INTERACTING BOSONS 2 2 BOSE–EINSTEIN CONDENSATION 2 3 HARTREE APPROXIMATION 2 4 LANDAU’S MEAN-?ELD THEORY 2 5 UPPER CRITICAL DIMENSION RENORMALIZATION GROUP 3 1 IDEA 3 2 MOMENTUM-SHELL TRANSFORMATION 3 3 ?-EXPANSION 3 4 DANGEROUSLY IRRELEVANT COUPLING 3 5 CORRECTIONS TO SCALING 3 6 FIELD-THEORETIC PERSPECTIVE 3 7 COMPUTATION OF ANOMALOUS DIMENSION 3 8 SUMMARY SUPERCONDUCTING TRANSITION 4 1 MEISSNER EFFECT 4 2 FLUCTUATION-INDUCED ?RST-ORDER TRANSITION 4 3 TYPE-II SUPERCONDUCTORS NEAR FOUR DIMENSIONS 4 4 ANOMALOUS DIMENSION FOR THE GAUGE ?ELD 4 5 WIDTH OF THE CRITICAL REGION NEAR LOWER CRITICAL DIMENSION 5 1 GOLDSTONE MODES 5 2 MERMIN–WAGNER–HOHENBERG THEOREM 5 3 NON-LINEAR ?-MODEL 5 4 LOW-TEMPERATURE EXPANSION 5 5 DISCUSSION KOSTERLITZ–THOULESS TRANSITION 6 1 VORTICES AND SPIN WAVES 6 2 MEAN-?ELD THEORY 6 3 DUALITY AND THE SINE-GORDON THEORY 6 4 RENORMALIZATION OF THE SINE-GORDON MODEL 6 5 UNIVERSAL JUMP OF SUPER?UID DENSITY 6 6 HEISENBERG MODEL DUALITY IN HIGHER DIMENSIONS 7 1 FROZEN LATTICE SUPERCONDUCTOR 7 2 CON?NEMENT OF MAGNETIC MONOPOLES 7 3 MAGNETIC ?ELD CORRELATIONS 7 4 COMPACT ELECTRODYNAMICS QUANTUM PHASE TRANSITIONS 8 1 DYNAMICAL CRITICAL EXPONENT 8 2 QUANTUM CRITICAL POINT IN 4-THEORY 8 3 BOSE–HUBBARD MODEL 8 4 QUANTUM ?UCTUATIONS AND THE SUPER?UID DENSITY 8 5 UNIVERSAL CONDUCTIVITY IN TWO DIMENSIONS