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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 | |