Nigel Goldenfeld

Lectures On Phase Transitions And The Renormalization Group (eBook, PDF)

• Format: PDF

Produktbeschreibung

Covering the elementary aspects of the physics of phases transitions and the renormalization group, this popular book is widely used both for core graduate statistical mechanics courses.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 420
• Erscheinungstermin: 8. März 2018
• Englisch
• ISBN-13: 9780429962042
• Artikelnr.: 54096255

Autorenporträt

Nigel Goldenfeld

Inhaltsangabe

Introduction * Scaling and Dimensional Analysis * Power Laws in Statistical Physics * Some Important Questions * Historical Development * Exercises How Phase Transitions Occur In Principle * Review of Statistical Mechanics * The Thermodynamic Limit * Phase Boundaries and Phase Transitions * The Role of Models * The Ising Model * Analytic Properties of the Ising Model * Symmetry Properties of the Ising Model * Existence of Phase Transitions * Spontaneous Symmetry Breaking * Ergodicity Breaking * Fluids * Lattice Gases * Equivalence in Statistical Mechanics * Miscellaneous Remarks * Exercises How Phase Transitions Occur In Practice * Ad Hoc Solution Methods * The Transfer Matrix * Phase Transitions * Thermodynamic Properties * Spatial Correlations * Low Temperature Expansion * Mean Field Theory * Exercises Critical Phenomena in Fluids * Thermodynamics * Two-Phase Coexistence * Vicinity of the Critical Point * Van der Waals Equation * Spatial Correlations * Measurement of Critical Exponents * Exercises Landau Theory * Order Parameters * Common Features of Mean Field Theories * Phenomenological Landau Theory * Continuous Phase Transitions * Inhomogeneous Systems * Correlation Functions * Exercises Fluctuations and the Breakdown of Landau Theory * Breakdown of Microscopic Landau Theory * Breakdown of Phenomenological Landau Theory * The Gaussian Approximation * Critical Exponents * Exercises Scaling in Static, Dynamic and Non-Equilibrium Phenomena * The Static-Scaling Hypothesis * Other Forms of the Scaling Hypothesis * Dynamic Critical Phenomena * Scaling in the Approach to Equilibrium * Summary The Renormalisation Group * Block Spins * Basic Ideas of the Renormalisation Group * Fixed Points * Origin of Scaling * RG in Differential Form * RG for the Two Dimensional Ising Model * First Order Transitions and Non-Critical Properties * RG for the Correlation Function * Crossover Phenomena * Correlations to Scaling * Finite Size Scaling Anomalous Dimensions Far From Equilibr