Lectures On Phase Transitions And The Renormalization Group

"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"

Autorentext

Nigel Goldenfeld

Inhalt

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