This NATO Advanced Study Institute held at Gei10, Norway, April 16th-27th 1979, was the fifth in a series devoted to the subject of phase transitions and instabilities. The application to NATO for the funding of this ASI contained the following para­ graphs: "Traditionally one has made a clear distinction between solids and liquids in terms of positional order, one being long-ranged and the other at most short-ranged. In recent years experiments have revealed a much more faceted picture and a less sharp distinction between solids and liquids. As an example one now has 3-dimensiona1 (3-D) liquids with 1-D density waves and 3-D solids with 1-D-1iquid molecular chains. The subsystems have the common feature of 10w­ dimensional systems: a strong tendency for fluctuations to appear. Although the connection between fluctuations and dimensionality, and the suppression of long-range order by fluctuations, was pointed out as early as 1935 by Peier1s and by Landau, it is in the last five years or so that theoretical work has gained momentum. This development of understanding started ten years ago, however, much inspired by the experimental work on 2-D spin systems.

Inhalt

Ordering in Strongly Fluctuating Systems: Introductory Comments.- 1. Introduction.- 2. A Theorist's Ideal Glass.- 3. Systems Far From Equilibrium.- Phase Transitions in Low-Dimensional Systems and Renormalization Group Theory.- 1. Phase Transitions and Some Simple Spin Models.- 2. Fluctuations and the Lower Critical Dimension.- 3. Values of Lower Critical Dimensionality for Some Spin Models.- 4. Fluctuations.- 5. Introduction to the Renormalization Group.- Real-Space Renormalization-Group Method for Quantum Systems.- Upper Marginal Dimensionality, Concept and Experiment.- 1. Phenomenological Description.- 2. Mean Field Theory.- 3. Ginzburg Criterion.- 4. Experiments on LiTbF4.- 5. Conclusion.- Lower Marginal Dimensionality. X-Ray Scattering from the Smectic-A Phase of Liquid Crystals.- 1. Introduction.- 2. The Nematic and Smectic A Phases of Liquid Crystals.- 3. The Correlation Function in the Harmonic Approximation.- 4. Experiment and Analysis.- 5. Results and Conclusions.- Appendix: Calculation of $$$$ in the SmA Phase.- Critical Fluctuations Under Shear Flow.- 1. Turbidity: TC change.- 2. The scattered light: Anisotropy; mean-field; lowering of UCD?.- 3. Discussion.- 4. "Moralité".- Lifshitz Points in Ising Systems with Competing Interactions.- 1. Introduction.- 2. One-dimensional Ising Systems with competing Interactions.- 3. Two-dimensional Ising systems.- 4. Conclusions.- Elementary Excitations in Magnetic Chains.- 1. Introduction.- 2. Magnons in XY-like Magnetic Chains.- 3. The Anisotropic, Classical XY Chain.- 3.1 The Model.- 3.2 Intuitive Analysis at Low Temperature for q = 2 and J = 0.- 3.3 Energy of a Wall.- 3.4 Number of Walls.- 3.5 Antiferromagnets in a Magnetic Field.- 4. A Simple Dynamical Model: The Almost - Ising Antiferromagnetic Chain.- 4.1 The Model.- 4.2 Collisions Between Two Solitons.- 5. Propagation of Broad Walls.- Experimental Studies of Linear and Nonlinear Modes in 1-D-Magnets.- 1. Real Systems; Experimental Methods.- 2. Linear Excitations.- 3. Nonlinear Excitations.- Q-Dependence of the Soliton Response in CsNiF3 At.- T = 10K and H =5kG.- Dynamics of the Sine-Gordon Chain: The Kink-Phonon Interaction, Soliton Diffusion and Dynamical Correlations.- 1. Statement of the Problem.- 2. A Kink-Phonon Collision.- 3. Diffusive Motion of the Kink.- 4. Dynamical Correlation Functions.- The Spin-Wave Continuum of the S=1/2 Linear Heisenberg Antiferrornagnet.- Excitations and Phase Transitions in Random Anti-Ferromagnets.- Neutron Scattering.- Critical Phenomena at Phase Transitions.- Percolation.- Excitations of Dilute Magnets Near the Percolation Threshold.- Critical Properties of the Mixed Ising Ferromagnet.- Structure and Phase Transitions in Physisorbed Monolayers.- History and Background.- Statistical Thermodynamics of Physical Adsorption.- Structural Investigations of Monolayers.- Substrate Influences.- Commensurate-Incommensurate Transition and Orientational Epitaxy.- Antiferromagnetism in 0« Films.- Conclusion.- Two-Dimensional Solids and Their Interaction with Substrates.- I. Collective Phenomena and Phase Transitions in Two Dimensions.- 1.1 Early Theoretical Works.- 1.2 Experimental Situation.- II. Effect of Substrate.- II.1 Two-Dimensional Solids and Adsorbed Layers.- II.2 Substrate Distortion and Related Effects.- II.3 Chemical Potential.- II.4 Substrate Potential.- II.5 Conclusion.- III. Walls and Domains.- III.1 A One-Dimensional Model.- III.2 The Theory of Frank and Van der Merwe.- III.3 Aubry's Theory.- III.4 Domains and Walls for Dimensions Larger than 1.- IV. The Pokrovskii-Talapov Model.- IV.1 Hypotheses.- IV.2 Solution.- IV.3 Bragg Singularities.- IV.4 The Pinning Transition.- V. Rate Gas Monolayers on Graphite or Lamellar Halides.- V.1 Introduction.- V.2 The Zero Temperature Theory of Bak, Mukamel, Villain and Wentowska.- V.3 Rare Gas Monolayers on Hexagonal Substrates at T i 0.- V.4 Effect of Substrate Distortions.- VI. The Novaco-Mc Tague Orientational Instability.- VI.1 General Argument.- VI.2 Case of Parallel Walls.- VI.3 Case of a Regular Network of Intersecting Walls.- VI.4 Finite Temperatures.- VI.5 Microscopic Theories.- Appendix A. Bragg Singularities of a 2-D, Harmonic Crystal.- Appendix B. Interaction between two Solutions.- Appendix C. Partition function of the Pokrovskii-Talapov Model Near the Commensurable-Incommensurable Transition.- Appendix D. Bragg Singularities of the Pokrovskii-Talapov Model Near the C-I Transition.- Appendix E. The Roughening Transition.- The Dislocation Theory of Melting: History, Status and Prognosis.- 1. Introduction.- 2. History.- 3. Status.- 4. Prognosis.- The Kosterlitz-Thouless Theory of Two-Dimensional Melting.- Phase Transitions and Orientational Order in a Two-Dimensional Lennard-Jones System.- The Roughening Transition.- I. Introduction.- II. The solid-On-Solid Model.- III. The BCF Argument.- IV. Experimental Results.- V. Monte Carlo Calculations: Qualitative Features.- VI. Static Critical Behavior.- VII. Roughening Dynamics and the Kosterlitz Renormalization Group Method.- VIII.The FSOS Model and Mc Calculations.- IX. Final Remarks.- Statics and Dynamics of the Roughening Transition: A Self-Consistent Calculation.- I. Introduction.- II. Roughening Transition.- III. Two-Dimensional Planar Model.- IV. Conclusions.- Fluctuations in Two-Dimensional Six-Vertex Systems.- Light Scattering Studies of the Two-Dimensional Phase Transition in Squaric Acid.- 1. Introduction.- 2. Light Scattering Studies.- 3. Order Parameter.- 4. Order Flucatuations.- 5. Peak Shape and Width.- 6. Disorder Induced Scattering.- 7. Conclusions.- Monte Carlo Simulation of Dilute Systems and of Two-Dimensional Systems.- I. Introduction.- II. Ferromagnets Diluted with Nonmagnetic Impurities and Related Systems.- III. Models for Quasi-Two-Dimensional (2D) Magnets.- IV. Lattice Gas Models for Adsorbed Monolayers at Surfaces.- Order and Fluctuations in Smectic Liquid Crystals.- I. Introduction.- II. The Nematic Phase.- III.The Nematic-Smectic A Transition and The Smectic A Phase.- IV. The Smectic C Phase and Smc-SmA Transition.- v. Liquid Crystals and Lower Dimensional Physics.- Dislocations and Disclinations in Smectic Systems.- Translational Defects.- Orientational Defects.- Non-Elementary Defects.- Observation of Dislocations.- Dislocation Motion.- "Pair Creation" of Disclinations.- Defects and Phase Transitions.- Fluctuations and Freezing in a One-Dimensional Liquid:Hg3-?AsF6.- The Model Hamiltonian.- High Temperature Properties (T > TC).- Long Range Order.- Dynamics.- The Effect of Pressure on the Modulated Phases of TTF-TCNQ.- Spin Glasses A Brief Review of Experiments, Theories, and Computer Simulations.- 1. Spin Glass Materials and Experiments.- 2. Theoretical Models and Concepts.- 3. Spin-Glass Freezing: Phase Transit…