Condensed Matter Physics and Exactly Soluble Models

A Survey by the Editors.- I.1 Violation of the Noncrossing Rule: The Hubbard Hamiltonian for Benzene.- I.2 Two Theorems on the Hubbard Model.- I.3 The Hubbard Model: Some Rigorous Results and Open Problems.- I.4 Flux Phase of the Half-Filled Band.- II.1 Proof of the Peierls Instability in One Dimension.- II.2 Stability of the Peierls Instability for Ring Shaped Molecules.- III.1 A Model for Crystallization: A Variation on the Hubbard Model.- III.2 Phase Separation due to Quantum Mechanical Correlations.- IV.1 Theory of Ferromagnetism and the Ordering of Electronic Energy Levels.- IV.2 Ordering Energy Levels of Interacting Spin Systems.- IV.3 Magnetic Properties of Some Itinerant-Electron Systems at T > 0.- V.1 Phase Transitions in Reservoir-Driven Open Systems with Applications to Lasers and Superconductors.- V.2 Equilibrium Statistical Mechanics of Matter Interacting with the Quantized Radiation Field.- V.3 Constructive Macroscopic Quantum Electrodynamics.- V.4 The Laser: A Reversible Quantum Dynamical System with Irreversible Classical Macroscopic Motion.- VI.1 A Proof of Part of Haldane's Conjecture on Spin Chains.- VI.2 Rigorous Results on Valence-Bond Ground States in Antiferromagnets.- VI.3 Valence Bond Ground States in Isotropic Quantum Antiferromagnets.- VI.4 Ground State Properties of a Fully Frustrated Quantum Spin System.- VII.1 Exact Ground State Energy of the Strong-Coupling Polaron.- VIII.1 Simplified Approach to the Ground-State Energy of an Imperfect Bose Gas.- VIII.2 Bose-Einstein Quantum Phase Transition in an Optical Lattice Model.- VIII.3 The Quantum-Mechanical Many-Body Problem: The Bose Gas.- Some of the Early History of Exactly Soluble Models.- IX.1 Exact Solution of the Problem of the Entropy of Two-Dimensional Ice.- IX.2 Exact Solution ofthe F Model of an Antiferroelectric.- IX.3 Exact Solution of the Two-Dimensional Slater KDP Model of a Ferroelectric.- IX.4 Residual Entropy of Square Ice.- IX.5 Two-Dimensional Ferroelectric Models.- IX.6 Relations Between the 'Percolation' and 'Colouring' Problem and Other Graph-Theoretical Problems Associated with Regular Planar Lattices: Some Exact Results for the 'Percolation' Problem.- IX.7 Analytic Properties of the Free Energy for the "Ice" Models.- X.1 Two-Dimensional Ising Model as a Soluble Problem of Many Fermions.- X.2 Solution of the Dimer Problem by the Transfer Matrix Method.- XI.1 Two Soluble Models of an Antiferromagnetic Chain.- XII.1 Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State.- XII.2 Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum.- XIII.1 Delta-Function Fermi Gas with Two-Spin Deviates.- XIII.2 Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model on One Dimension.- XIV.1 Exact Solution of a Many-Fermion System and Its Associated Boson Field.- Selecta of Elliott H. Lieb.- Publications of Elliott H. Lieb.