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Introduction | |
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Fundamentals of Statistical Physics | |
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The Lectures--A Survey | |
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The Journey: Many Different Approaches | |
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The Main Sights | |
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Is the Trip Worthwhile? | |
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One Particle and Many | |
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Formulation | |
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The Ising Model | |
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N Independent Particles--Quantum Description | |
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Averages From Derivatives | |
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N Independent Particles in a Box | |
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Fluctuations Big and Small | |
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The Problems of Statistical Physics | |
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Gaussian Distributions | |
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Introduction | |
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One Variable | |
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Many Gaussian Variables | |
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Lattice Green Function | |
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Gaussian Random Functions | |
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Central Limit Theorem | |
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Distribution of Energies | |
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Large Deviations | |
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On Almost Gaussian Integrals | |
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Three Versions of Gaussian Problems | |
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Quantum Mechanics and Lattices | |
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All of Quantum Mechanics in One Brief Section | |
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From d = 1 Models to Quantum Mechanics | |
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An Example: The Linear Ising Chain | |
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One-Dimensional Gaussian Model | |
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Coherence Length | |
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Operator Averages | |
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Correlation Functions | |
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Ising Correlations | |
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Two-Dimensional Ising Model | |
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Random Dynamics | |
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Diffusion and Hopping | |
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Random Walk on a Lattice | |
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Formulating This Problem | |
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The Diffusion of Probability and Particles | |
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From Conservation to Hydrodynamic Equations | |
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Distribution Functions | |
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Cascade Processes and Securities Prices | |
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Reprints on Dynamics | |
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Forest and Witten: Smoke Particle Aggregates | |
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Witten and Sander: Diffusion Limited Aggregation | |
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Kadanoff: Chaos and Complexity | |
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From Hops to Statistical Mechanics | |
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Random Walk in Momentum | |
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The Diffusion Equation Again | |
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Time Dependence of Probability | |
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Time Dependence in Deterministic Case | |
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Equilibrium Solutions | |
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Back to Collisions | |
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From Fokker-Planck to Equilibrium | |
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Properties of Fokker-Planck Equation | |
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Reprints on Organization | |
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Chao Tang et al.: Phase Organization | |
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Bak et al.: Self-Organized Criticality | |
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Carlson et al.: Singular Diffusion | |
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Jaeger et al.: Experimental Studies | |
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Correlations and Response | |
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Time Independent Response | |
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Hamiltonian Time-Dependence | |
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Sum Rules | |
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Non-Interacting Particles | |
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Plasma Behavior | |
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More Statistical Mechanics | |
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Statistical Thermodynamics | |
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The Chemical Potential Defined | |
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Barometer Formula | |
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Sharing Energy | |
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Ensemble Theory | |
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Temperatures and Energy Flow | |
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Fermi, Bose, and Other | |
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Quantum Formulation | |
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Statistical Mechanics of Non-Interacting Degenerate Particles | |
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The Non-Degenerate Limit | |
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Degenerate Fermions | |
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Degenerate Bosons I. Photons and Phonons | |
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Degenerate Bosons II. One-Dimensional Phonons | |
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Degenerate Bosons III. Bose Phase Transition | |
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Entropies | |
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Phase Transitions | |
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Overview of Phase Transitions | |
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Thermodynamic Phases | |
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Phase Transitions | |
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Two Kinds of Transitions | |
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Back to the Ising Model | |
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Mean Field Theory of Magnets | |
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The Phases | |
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Low Temperature Result | |
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Free Energy Selection Argument | |
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Behaviors of Different Phases | |
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Mean Field Theory of Critical Behavior | |
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The Infinite Range Model | |
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Mean Field Theory Near the Critical Point | |
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Critical Indices | |
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Scaling Function for Magnetization | |
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Spatial Correlations | |
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Analyticity | |
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Mean Field Theory for the Free Energy | |
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When Mean Field Theory Fails | |
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Continuous Phase Transitions | |
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Historical Background | |
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Widom Scaling Theory | |
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The Ising Model: Rescaled | |
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Fixed Points | |
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Phenomenology of Scaling Fields | |
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Theory of Scaling Fields | |
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Scaling Relations for Operators | |
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Transforming Operators | |
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Universality | |
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Operator Product Expansions | |
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Reprints on Critical Correlations | |
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Kadanoff: Correlations Along a Line | |
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Kadanoff-Wegner: Marginal Behavior | |
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Renormalization in One Dimension | |
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Introduction | |
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Decimation | |
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The Ising Example | |
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Phase Diagrams, Flow Diagrams, and the Coherence Length | |
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The Gaussian Model | |
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Analysis of Recursion Relation | |
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Fixed Point Analysis for the Gaussian Model | |
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Two-Dimensional Ising Model | |
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Real Space Renormalization Techniques | |
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Introduction | |
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Decimation: An Exact Calculation | |
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The Method of Neglect | |
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Potential Moving | |
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Further Work | |
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Reprints on Real Space RG | |
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Niemeijer and van Leeuwen: Triangular Lattice R.G. | |
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David Nelson's Early Summary | |
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Kadanoff: Bond-moving, and a Variational Method | |
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Kadanoff: Migdal's Simple and Versatile Method | |
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Migdal's Original Papers | |
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Duality | |
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Doing Sums | |
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Two Dimensions | |
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Direct Coupling and Dual Coupling | |
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Two-Dimensional Calculation | |
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Ising Model | |
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XY is Connected to SOS | |
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Gaussian goes into Gaussian | |
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Dual Correlations | |
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Planar Model and Coulomb Systems | |
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Why Study a Planar Model? | |
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One-Dimensional Case | |
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Phases of the Planar Model | |
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The Gaussian Approximation | |
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Two-Dimensional Coulomb Systems | |
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Multipole Expansion | |
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Reprint on Spin Waves | |
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V. L. Berezinskii: An Overview of Problems with Continuous Symmetry | |
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XY Model, Renormalization, and Duality | |
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Plan of Action | |
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Villain Representation of the Basic Bonds | |
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Duality Transformation | |
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Two Limits | |
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Vortex Representation | |
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The Magnetically Charged System | |
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Correlation Calculation | |
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The Renormalization Calculation | |
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Spatial Averages | |
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The Actual Renormalization | |
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Reprints on Planar Model | |
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The Kosterlitz-Thouless Theory | |
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Kosterlitz: On Renormalization of the Planar Model | |
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Jorge V. Jose, Leo P. Kadanoff, Scott Kirkpatrick, David R. Nelson: Renormalization and Vortices | |
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Index | |