Nigel Goldenfeld

Lectures On Phase Transitions And The Renormalization Group

• Broschiertes Buch

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 as well as for"

Produktdetails

• Verlag: Taylor & Francis Inc
• Seitenzahl: 416
• Erscheinungstermin: 30. Juni 1972
• Englisch
• Abmessung: 229mm x 152mm x 24mm
• Gewicht: 596g
• ISBN-13: 9780201554090
• ISBN-10: 0201554097
• Artikelnr.: 22282470

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 Equilibrium
Introduction
Similarity Solutions
Anomalous Dimensions in Similarity Solutions
Renormalisation
Perturbation Theory for Barenblatts Equation
Fixed Points
Conclusion Continuous Symmetry
Correlation in the Ordered Phase
Kosterlitz-Thouless Transition Critical Phenomena Near Four Dimensions
Basic Idea of the Epsilon Expansion
RG for the Gaussian Model
RG Beyond the Gaussian Approximation
Feyman Diagrams
The RG Recursion Relations
Conclusion