The Casimir effect in critical systems / Michael Krech.

Format:

Book

Author/Creator:

Krech, Michael.

Language:

English

Subjects (All):

Critical phenomena (Physics).

Casimir effect.

Finite size scaling (Statistical physics).

Physical Description:

x, 253 pages : illustrations ; 23 cm

Place of Publication:

Singapore ; New Jersey : World Scientific, [1994]

Summary:

The well-known Casimir effect has a direct analogue in systems near critical or multicritical points. Critical fluctuations in systems confined to finite geometries lead to attractive or replusive forces between the system boundaries. These forces influence the formation of wetting layers of liquid [superscript 4]He or binary liquid mixtures near critical points in these fluids. With the aid of recently developed versions of the atomic force microscope these forces appear to be directly measurable. This book contains an introduction to the physics of critical phenomena and reviews the most recent developments in the theory of finite-size scaling. A detailed discussion of the Casimir effect and related questions follows. The analysis of quantitative effects on the specific heat of critical films, the formation of wetting layers, and force measurements finishes the presentation. Book jacket.

Contents:

1.1 Bulk Critical Phenomena 1

1.1.1 Critical End Points 6

1.1.2 Tricritical Points 9

1.1.3 Universality and Critical Exponents 12

1.1.4 The Free Energy 16

1.2 Surface Critical Phenomena 17

1.2.1 The Surface Tension 21

1.2.2 Surface Universality Classes 23

1.2.3 Surface Critical Exponents 24

1.3 Finite Size Systems 26

1.3.1 Critical Films 28

1.3.2 Critical Fluids in Capillaries 29

1.3.3 Critical Fluids in Pores 30

1.4 Theoretical Concepts 30

1.4.1 Lattice Models and Universality 31

1.4.2 The Order Parameter Concept 36

1.4.3 Continuum Models 39

2 Finite Size Scaling 43

2.1 Phenomenology 43

2.1.1 Logarithmic Corrections 49

2.1.2 Interfacial Tensions and the Helicity Modulus 51

2.1.3 Curvature Effects 54

2.2 Lattice Models in Finite Geometries 55

2.2.1 The Ising Model 56

2.2.2 The XY - and the Heisenberg Model 61

2.2.3 The Potts Model 65

2.2.4 The Spherical Model 67

2.3 Continuum Theory in Finite Geometries 72

2.3.1 The Ginzburg - Landau Hamiltonian 72

2.3.2 Mean Field Theory 74

2.3.3 The Renormalization Group 78

2.3.4 Conformal Field Theory in Two Dimensions 81

3 The Casimir Effect 85

3.1.1 The Casimir Effect in Dielectric Media 88

3.1.2 The Casimir Effect in Statistical Systems 92

3.2 The Casimir Effect in Critical Films 94

3.2.1 The Critical Casimir Amplitudes 96

3.2.2 The Tricritical Casimir Amplitudes 102

3.3 Conformal Invariance 103

3.3.1 Correlation Functions and Primary Scaling Operators 106

3.3.2 The Stress Tensor 109

3.4 The Casimir Effect and the Stress Tensor 113

3.4.1 The Casimir Amplitudes in Critical Strips 115

3.4.2 The Casimir Amplitudes in Critical Films 118

4 Wall Effects in Critical Films 120

4.1 Distant Wall Corrections 121

4.1.1 Distant Wall Corrections and Conformal Invariance 123

4.2 The Energy Density Profiles 126

4.2.1 The Scaling Functions 129

4.2.2 Wall Effects 134

4.3 Short Distance Expansion of the Energy Density 136

4.3.1 Surface Operators 137

4.3.2 The Expansion Coefficients 140

4.4 The Short Distance Expansion and the Central Charge 144

5 The Finite Size Scaling Functions 148

5.1 Universality and Scaling Functions 148

5.1.1 Finite Size Scaling and the Bulk Correlation Length 152

5.1.2 Bulk, Surface, and Finite Size Contributions 153

5.2 Surface Tensions near Critical End Points 155

5.3 T > T[subscript c,b]: The Scaling Functions [Theta subscript +] 158

5.3.1 Above Bulk Criticality 159

5.3.2 Above Bulk Tricriticality 166

5.4 T < T[subscript c,b]: The Scaling Functions [Theta subscript -] 169

5.4.1 Below Bulk Criticality 171

5.4.2 Limitations of the [epsilon]-Expansion 177

5.5 The Dimensional Crossover 179

5.5.1 Completely Finite and One Dimensional Geometries 180

5.5.2 Geometries with Two or More Infinite Extensions 183

6 Experiments on Finite Size Scaling 185

6.1 The Specific Heat 185

6.1.1 [superscript 4]He in Critical Films 189

6.1.2 [superscript 4]He in Capillaries and Pores 191

6.1.3 [superscript 3]He - [superscript 4]He Mixtures in Tricritical Films 193

6.2 The Superfluid Density in Confined [superscript 4]He 196

6.2.1 The Superfluid Density in Films 197

6.2.2 The Superfluid Density in Capillaries and Pores 198

6.3 Wetting Phenomena near Criticality 199

6.3.1 Critical [superscript 4]He on Substrates 203

6.3.2 Tricritical [superscript 3]He - [superscript 4]He Mixtures on Substrates 214

6.3.3 Binary Liquid Mixtures on Substrates 215

6.4 The Casimir Force 217

6.4.1 Critical [superscript 4]He between Plates 219

6.4.2 Tricritical [superscript 3]He - [superscript 4]He Mixtures between Plates 221

6.4.3 Binary Liquid Mixtures between Plates 223

7.1 The Casimir Effect 225

7.2 Wall Effects and Profiles 226

7.3 The Finite Size Scaling Functions 227

7.4 Other Geometries 228

7.5 Correlation Functions and Critical Dynamics 228.

Notes:

Includes bibliographical references and index.

ISBN:

9810218451

OCLC:

31225799