Preface to the First Edition -- Preface to the Second Edition -- CONTENTS -- Chapter 1 The Statistical Mechanics of Membranes and Interfaces David R. Nelson -- 1. Flat Surfaces -- 1.1. The Roughening Transition -- 1.2. Wetting Transitions -- 2. Crumpled Membranes -- 2.1. Experimental Realizations -- 2.2. Plaquette Surfaces -- 2.3. Perturbation Theory for Tethered Surfaces -- References -- Chapter 2 Interfaces: Fluctuations, Interactions and Related Transitions Michael E. Fisher -- Introduction -- 1. Interface Models, Mean Field Theory, and Wetting -- 1.1. Levels of Theory -- 1.2. Mean Field Theory for Order Parameters -- 1.3. Derivation of Interface Models -- 1.4. External Forces -- 1.5. The Complete Wetting Transition -- 1.6. Wall Effects and the Interface Hamiltonian -- 1.7. Wetting Transitions with Short-range Forces: Mean Field Theory -- 2. Fluctuations and Steric Repulsions -- 2.1. The Wandering Exponent -- 2.2. Interfaces in Two-dimensions: Random Walks -- 2.3. Correlations and Correlation Lengths -- 2.4. The Stiffening or Roughening Transition -- 2.5. Random Media -- 2.6. Fluctuations at Complete Wetting under Long-range Forces -- 2.7. Constrained Interfaces and the Wall-interface Potential -- 2.8. Membranes -- 2.9. Checks of the Wall-interface Potential -- 2.10. Complete Wetting Revisited -- 2.11. Many Walls and the Shape of a Vicinal Crystal Face -- 3. Critical Wetting and Renormalization Groups for Interfaces -- 3.1. Critical Wetting in d = 2 Dimensions -- 3.2. Renormalization Groups for Critical Wetting -- 3.3. The Linearized Functional Renormalization Group -- 3.4. Critical Wetting in d = 3 Dimensions -- 3.5. Test of the d = 3 Critical Wetting Predictions -- 3.6. Approximate Nonlinear Renormalization Group -- 3.7. Numerical Studies -- 3.8. Approach to d = 3: Anomalous Bifurcation -- 3.9. Concluding Remarks -- References.

Chapter 3 Equilibrium Statistical Mechanics of Fluctuating Films and Membranes Stanislas Leibler -- Introduction -- 1. Cell Membranes as an Inspiration for Physics -- 1.1. A History of the Discovery of Membrane Structure: A Few Basic Facts about Membranes -- 1.2. Some Physical Properties of Membranes and Amphiphilic Films -- (1) The amphiphilic nature of the constituents. -- (ii) Fluidity of the membranes. -- (iii) The possibility of topology variations -- 2. The Elastic Properties of Fluid Membranes and the Shapes of Vesicles -- 2.1. Curvature Energy and a Simple Elastic Model -- 2.2. Shapes and Fluctuations of Vesicles -- 2.3. Measuring of Elastic Constants -- 3. The Role of Thermal Fluctuations in the Behavior of (Fluid) Membranes and Films -- 3.1. Fluctuations of a Single Fluid Membrane -- 3.2. Perturbation Calculations and the Concept of Crumpling Transition -- 3.3. The Thermodynamic Behavior of an Ensemble of Fluid Membranes -- 4. Unbinding Transitions and the Swelling of Lamellar Phases -- 4.1. Molecular Forces between Membranes -- 4.2. Fluctuations-Induced Interactions -- 4.3. The Competition between Molecular and Fluctuation-Induced Interactions: Functional Renormalization -- 4.4. Complete versus Incomplete Unbinding and the Swelling of Lamellar Phases -- 4.5. The Critical Unbinding Transition -- 5. Membranes with Internal Degrees of Freedom -- 5.1. The "Membranology" of f-Membrane Systems -- 5.2. Curvature Instability in Fluid Membranes -- 5.3. The Polymorphism of Lipid/Water Systems: Different Kinds of f-Membranes -- 5.4. Towards a Mean-Field Theory of Lamellar Phases -- 5.5. Cubic Phases as Crystals of f-Membranes -- References -- Chapter 4 The Physics of Microemulsions and Amphiphilic Monolayers David Andelman -- Abstract -- Acknowledgments -- References -- Chapter 5 Properties of Tethered Surfaces Yacov Kantor -- 1. Introduction.

1.1. What is a "Tethered Surface"? -- 1.2. The Tethered Surface as a Polymer -- 2. Phantom Chains and Networks -- 2.1. Linear Polymers -- 2.2. Gaussian Networks and Surfaces -- 2.3. Properties of Phantom Tethered Surfaces -- 3. Excluded Volume Effects -- 3.1. Bounds on the Exponent ν -- 3.2. Analytic Estimates of ν -- 3.3. Monte Carlo Investigation of Tethered Surfaces -- 4. Crumpling Transition in Tethered Surfaces -- 4.1. Very Rigid and Very Flexible Surfaces -- 4.2. Excluded Volume Effects -- 5. Concluding Remarks -- 5.1. Summary and Discussion -- 5.2. What Next? -- References -- Chapter 6 Theory of the Crumpling Transition David R. Nelson -- 1. Normal-Normal Correlation in Liquid Membranes -- 2. Tethered Surfaces with Bending Energy -- 3. Landau Theory of the Crumpling Transition -- 4. Defects and Hexatic Order in Membranes -- References -- Chapter 7 Geometry and Field Theory of Random Surfaces and Membranes Fran¸cois David -- 1. Introduction -- 2. Differential Geometry for Surfaces -- 2.1. Surfaces, Tangent Vectors, Tensors -- 2.2. Geodesics, Parallel Transport, Covariant Derivatives -- 2.3. Integration, Stokes Formula -- 2.4. Extrinsic Curvature -- 2.5. The Riemann Curvature Tensor -- 2.6. The Gauss-Bonnet Theorem -- 2.7. Minimal Surfaces -- 2.8. Conformal (or Isothermal) Coordinates -- 3. Fields on Surfaces -- 3.1. Free Field -- 3.2. The Heat Kernel Regularization -- 3.3. The Conformal Anomaly and the Liouville Action -- 4. Fluid Membranes Models -- 4.1. Continuous Model for Fluid Membranes -- 4.2. Partition Function, Gauge Fixing -- 4.3. Effective Action and the Background Field Method -- 4.4. Renormalization of the Bending and Gaussian Rigidity -- 4.5. Renormalization of the Surface Tension -- 4.6. Effect of Tangential Flows -- 5. Fluid Membranes: Non-Perturbative Issues and the Large d Limit -- 5.1. The Large d Limit.

5.2. Planar Configuration -- 5.3. Renormalization Group Behavior -- 5.4. Conformal Fluctuations and Instabilities -- 6. Effective Models for Fluid Membranes and Strings -- 6.1. The Polyakov String Model -- 6.2. The Liouville Model -- 6.3. Discretized Models for Surfaces -- 7. Hexatic Membranes -- 7.1. Hexatic Membranes: Continuous Model -- 7.2. Hexatic Membranes: Renormalization Group Behavior -- 8. Crystalline Membranes -- References -- Chapter 8 Statistical Mechanics of Self-Avoiding Crumpled Manifolds - Part I Bertrand Duplantier -- 1. Continuum Model of Self-Avoiding Manifolds -- 1.1. Edwards Model -- 1.2. Gaussian D-Dimensional Manifold -- 1.3. Dimensional Analysis -- 1.4. Higher Order Interactions -- 1.5. Analytical Continuation in Dimension and Regularization -- 1.6. Extension to Negative Dimensions -- 2. Perturbation Expansion -- 2.1. Rules -- 2.2. Divergences -- 2.2.1. End-to-end Distance -- 2.2.2. Partition Function -- 2.2.3. Dimensional Regularization -- 3. Direct Renormalization -- 3.1. Scaling Functions -- 3.2. Second Virial Coefficient -- 3.3. Critical Exponents -- 4. Contact Exponents -- 5. On the Nonuniversality of Exponent γ -- 6. Conclusion -- References -- Chapter 9 Statistical Mechanics of Self-Avoiding Crumpled Manifolds - Part II Bertrand Duplantier -- 1. Interacting Manifold Renormalization: A Brief History -- 2. Manifold Model with Local δ Interaction -- 2.1. Perturbative Expansion -- 2.2. Second Virial Coefficient -- 2.3. Resummation of Leading Divergences -- 2.4. Comparison to One-Loop Renormalization -- 2.5. Analytic Continuation in D of the Euclidean Measure -- 2.6. Analysis of Divergences -- 2.7. Factorizations -- 2.8. Renormalization -- 3. Self-Avoiding Manifolds and Edwards Models -- 3.1. Introduction -- 3.2. Renormalizability to First Order -- 3.3. Renormalizability to All Orders.

3.4. Perturbation Theory and Dipole Representation -- 3.5. Singular Configurations and Electrostatics in RD -- 3.6. Multi-local Operator Product Expansion -- 3.7. Power Counting and Renormalization -- 3.8. Finite Size Scaling and Direct Renormalization -- 3.9. Hyperscaling -- 3.10. Θ-Point and Long-Range Interactions -- Acknowledgments -- References -- Chapter 10 Anisotropic and Heterogeneous Polymerized Membranes Leo Radzihovsky -- 1. Preamble -- 2. Anisotropic Polymerized Membranes -- 2.1. Motivation and Introduction -- 2.2. Model -- 2.3. Mean-field theory -- 2.4. Fluctuations and Self-avoidance in the Crumpled and Flat Phases -- 2.4.1. Anomalous Elasticity of the Flat Phase -- 2.4.2. SCSA of the Flat Phase -- 2.5. Fluctuations in "Phantom" Tubules -- 2.5.1. Anomalous Elasticity of the Tubule Phase -- 2.5.2. Zero-modes and Tubule Shape Correlation -- 2.6. Self-avoidance in the Tubule Phase -- 2.6.1. Flory Theory -- 2.6.2. Renormalization Group and Scaling Relations -- 2.7. Phase Transitions -- 2.7.1. Renormalization Group Analysis of Crumpled-To-Tubule Transition -- 2.7.2. Scaling Theory of Crumpled-To-Tubule and Tubule-To-Flat Transitions -- 3. Random Heterogeneity in Polymerized Membranes -- 3.1. Motivation -- 3.2. Model of a Heterogeneous Polymerized Membrane -- 3.3. Weak Quenched Disorder: "Flat-glass" -- 3.3.1. Short-range Disorder -- 3.3.2. Long-range Disorder -- 3.4. Strong Quenched Disorder: "Crumpled-glass" -- 4. Interplay of Anisotropy and Heterogeneity: Nematic Elastomer Membranes -- 5. Summary -- 6. Acknowledgments -- References -- Chapter 11 Fixed-Connectivity Membranes Mark J. Bowick -- 1. Introduction -- 2. Physical Examples of Membranes -- 3. Phase Diagrams -- 3.1. Phantom Membranes -- 3.1.1. The Crumpled Phase -- 3.1.2. The Crumpling Transition -- 3.1.3. The Flat Phase -- 3.1.4. The Properties of the Flat Phase.

3.2. Self-avoiding Membranes.