More is Different

PREFACE: N. PHUAN ONG AND RAVIN N. BHATT xi 1950 TO Y2K: E.ABRAHAMS xv 1. MORE is DIFFERENT - ONE MORE TIME 1 PHILIP W. ANDERSON 1 2 LOCALIZATION YESTERDAY, TODAY, TOMORROW 9 T. V. RAMAKRISHNAN 9 2.1 ABSENCE OF DIFFUSION IN RANDOM LATTICES 9 2.1.1 EXPERIMENTAL BACKGROUND 9 2.1.2 THE LOCALIZATION IDEA 10 2.1.3 RELATED DEVELOPMENTS 11 2.1.4 CONSEQUENCES OF LOCALIZATION 12 2.1.5 LOCALIZATION AS A GENERAL FEATURE OF DISORDER 13 2.2 SCALING AND WEAK LOCALIZATION 14 2.2.1 THOULESS CONDUCTANCE 14 2.2.2 SCALING THEORY 15 2.2.3 WEAK LOCALIZATION 16 2.2.4 THEORETICAL DEVELOPMENTS 18 2.2.5 MESOSCOPIC SYSTEMS AND PHENOMENA 21 2.2.6 OTHER EXCITATIONS 21 2.2.7 SUMMARY 22 2.3 TOMORROW 23 2.3.1 GLASS AND SPIN GLASS 23 2.3.2 SUPERCONDUCTOR-INSULATOR TRANSITION 23 2.3.3 METAL-INSULATOR TRANSITION IN 2D 24 2.3.4 DECOHFRENCE IN DISORDERED CONDUCTORS 25 2.3.5 LOCALIZATION IN MANGANITES 27 3 METAL-INSULATOR TRANSITIONS IN DISORDERED SYSTEMS 33 MYRIAM P. SARACHIK 33 3.1 CRITICAL ExPONENT PUZZLE IN 3D 33 3.2 NOVEL PHENOMENA IN DILUTE 2D SYSTEMS: NEW PHYSICS OR OLD? 33 4 THE NATURE OF SUPERFLUID 3HE IN SILICA AEROGEL 47 D. D. OSHEROFF, B. 1. BARKER, AND Y. LEE 47 4.1 INTRODUCTION 47 4.2 RESULTS OF THE FIRST STUDY 51 4.3 RESULTS OF THE SECOND STUDY 54 4.4 COMPARISON WITH PREVIOUS RESULTS 59 4.5 CONCLUSIONS 61 5 RVB DESCRIPTION OF HIGH-T, SUPERCONDUCTORS 63 PATRICK A. LEE 63 5.1 INTRODUCTION 63 5.2 REVIEW OF RVB THEORY 64 5.3 PROJECTED WAVEFUNCTIONS AND STAGGERED CURRENT FLUCTUATIONS 68 5.4 CONCLUSION 73 6. ANGLE-RESOLVED PHOTOEMISSION RESULTS IN CUPRATES 75 J. C. CAMPUZANO 75 6.1 INTRODUCTION 75 6.2 NATURE OF THE ELECTRONIC STATES 76 6.3 EXCITATIONS AT THE FERMI SURFACE 77 6.4 QUASIPARTICLES IN THE SUPERCONDUCTING STATE 80 6.5 NEW ENERGY SCALES IN THE SUPERCONDUCTING STATE 82 7. SPIN EXCITATIONS IN COPPER OXIDE SUPERCONDUCTORS 91 B. KEIMER 91 7.1 INTRODUCTION 91 7,2 NEUTRON SPECTROSCOPY RESULTS IN CUPRATES 92 7.3 STRIPE FORMATION IN LA2-xSRxCU04 94 7.4 MAGNETIC RESONANCE PEAK IN CUPRATES 95 7.5 ORIGIN OF THE RESONANCE PEAK 97 7.6 CONCLUSION 100 8. ANDERSON'S THEORY OF HIGH-T, SUPERCONDUCTIVITY 103 G.BASKARAN 103 8.1 INTRODUCTION 103 8.2 THE RVB THEORY OF 1987 104 8.3 THREE APECTS OF ANDERSON'S 1987 MECHANISM 110 8.4 SOME COMMENTS ON ANDERSON'S SOLUTION 112 8.5 APPENDIX 113 9 QUANTUM CONFINEMENT AND CUPRATE CRITICALITY 121 T. SENTHIL AND MATTHEW P. A. FISHER 121 9.1 INTRODUCTION 121 9.2 EXPERIMENTS 122 9.3 NOVEL EXCITATIONS 122 9.4 THE Z2 GAUGE THEORY. 123 9.5 PHASE DIAGRAM. 123 9.6 CHARGON CONDENSATION AND SUPERCONDUCTIVITY 127 9.7 QUANTUM CONFINEMENT CRITICAL POINT 128 9.8 EXPERIMENTAL IMPLICATIONS 130 9.9 COMPARISON WITH ANDERSON'S RVB STATE 132 10 SPIN-TRIPLET SUPERCONDUCTIVITY OF SR2RuO4 135 Y. MAENO 135 10.1 INTRODUCTION 135 10.2 QUASI-21) FERMI LIQUID PROPERTIES 137 10.3 SPIN-TRIPLET SUPERCONDUCTIVITY. 138 10.4 ANISOTROPY OF THE SUPERCONDUCTING GAP 141 10.5 H - T PHASE DIAGRAM 143 10.6 CONCLUDING REMARKS 146 11 TRIPLET QUASI-ONE-DIMENSIONAL SUPERCONDUCTORS 151 S. E. BROWN, M. J. NAUGHTON, 1. J. LEE, E. 1. CHASHECHKINA, AND P. M. CHAIKIN 151 11.1 INTRODUCTION 151 11.2 EARLY RESULTS ON P-WAVE PAIRING. 153 11.3 DIMENSIONALITY REDUCTION IN A MAGNETIC FIELD 154 11.4 INTERLAYER DECOUPLING 156 11.5 RECENT EXPERIMENTS ON SPIN PAIRING 161 11.6 CONCLUSIONS 169 12 MAGNETIC MOMENTS IN METALS 173 H. R. OTT 173 12.1 INTRODUCTION 173 12.2 HEAVY (SLow) ELECTRONS 177 12.3 COEXISTENCE OF MAGNETIC ORDER AND HEAVY ELECTRONS 180 12.4 NON-FERMI-LIQUID FEATURES OF HEAVY-ELECTRON METALS 182 12.5 SUPERCONDUCTIVITY OF HEAVY ELECTRON METALS 183 12.6 CONCLUSIONS 186 13 SUPERCONDUCTIVITY AND MAGNETISM IN HEAVY-FERMIONS 191 F. STEGLICH el al. 191 13.1 INTRODUCTION 192 13.2 MAGNETIC -EXCITON MEDIATED SUPERCONDUCTIVITY 194 13.3 ANTIFERROMAGNETISM AND SUPERCONDUCTIVITY 197 13.4 HEAVY-FERMION METALS NEAR A MAGNETIC INSTABILITY 203 13.5 OUTLOOK. 206 14 THE MOTT TRANSITION 211 G. KOTLIAR 211 14.1 INTRODUCTION 211 14.2 MODEL HAMILTONIAN 212 14.3 MEAN FIELD THEORY 214 14.4 SPECTRAL FUNCTIONS OF STRONGLY CORRELATED STATES 219 14.5 ANOMALOUS RESISTIVITY AND SPECTRAL WEIGHT 222 14.6 THE MOTT TRANSITION AS A BIFURCATION 226 14.7 EXTENSIONS OF DYNAMICAL MEAN FIELD METHODS 230 14.8 CONCLUSIONS 232 15 FIRST STEPS IN GLASS THEORY 237 MARC WZARD 237 15.1 INTRODUCTION 237 15.2 MATHEMATICS 237 15.3 EXPERIMENTS 238 15.4 A MEAN-FIELD SPIN-GLASS ANALOGY 240 15.5 A LESSON FROM MEAN-FIFLD: MANY VALLEYS 243 15.6 BEYOND THE ANALOGY: FIRST- PRINCIPLES COMPUTATION 246 15.7 CONCLUSION 251 16 GEOMETRICAL FRUSTRATION AND MARGINAL CONSTRAINT 255 A. P. RAMIREZ 255 16.1 INTRODUCTION 255 16.2 GEOMETRICAL FRUSTRATION 256 16.3 ORDINARY WATER ICE 259 16.4 SPIN ICE IN PYROCHLORES 260 16.5 KAGOME-LIKE SYSTEMS 262 16.6 GEOMETRICAL FRUSTRATION IN NON-MAGNETIC SYSTEMS 264 17 OLFACTION AND COLOR VISION: MORE IS SIMPLER 269 J. J. HOPFIELD 269 17.1 COLOR VISION 270 17.2 OLFACTION 271 17.3 COMPARATIVE PROBLEMS OF VISION AND OLFACTION 272 17.4 THE LOGARITHMIC DISTRIBUTION OF ODORANT BINDING CONSTANTS 272 17.5 ODORANT MODELING 273 17.6 OLFACTORY TASKS IN A LEAST-SQUARED ERROR ALGORITHM 275 17.7 AN APPROACH THROUGH LARGE-n 276 17.8 ON THE LARGE NUMBER n OF CELL TYPES: MORE IS SIMPLER 280 17.9 SEPARATION OF TWO UNKNOWN ODORS 281 17.10 MORE IS SIMPLER 284 18 SCREENING AND GIANT CHARGE INVERSION IN ELECTROLYTES 285 T. T. NGUYEN, A. Yu. GROSBERG, AND B. 1. SHKLOVSKII 285 18.1 INTRODUCTION 285 18.2 SCREENING OF CHARGED SURFACE BY SPHERICAL Z-IONS. 292 18.3 LONG CHARGED RODS AS Z-IONS 297 19 FOREST FIRES AND LUMINOUS MATTER IN THE UNIVERSE 301 PER BAK AND KAN CHEN 301 19.1 INTRODUCTION 302 19.2 THE FOREST FIRE MODEL 303 19.3 SCALE-DEPENDENT DIMENSION OF LUMINOUS MATTER 306 19.4 FOREST FIRES AND MEASLES 310 20 COMPLEXITY IN COSMOLOGY 313 L. PIETRONERo el aL 313 20.1 INTRODUCTION 313 20.2 FRACTAL STRUCTURES AND SELF ORGANIZATION 314 20.3 RECONSTRUCTING THE PUZZLE 319 20.3.1 SCALING PROPERTIES AND DATA ANALYSIS. 321 20.3.2 IMPLICATIONS OF FRACTAL STRUCTURE UP TO Ao 324 20.4 FRACTAL COSMOLOGY IN AN OPEN UNIVERSE 326 21 STATISTICAL PHYSICS AND COMPUTATIONAL COMPLEXITY 331 S. KIRKPATRICK AND B. SELMAN 331 21.1 INTRODUCTION 331 21.2 SATISFIABILITY AND HARD-PROBLEM INSTANCES 332 21.3 CONNECTIONS TO STATISTICAL PHYSICS 336 21.4 A CLOSER LOOK AT THE PHASE TRANSITION. 337 21.5 MIXTURES OF 2-SAT AND 3-SAT PROBLEMS. 339

N.-Phuan Ong is Professor of Physics and Ravin N. Bhatt is Professor of Electrical Engineering at Princeton University Both are affiliated with the Princeton Materials Institute.