Spis treści: Exactly Solved Models: A Journey In Statistical Mechanics

Introduction by C. N. Yang, s. v
Preface, s. ix

1. Dimer Statistics

  • Introduction, s. 3
  • The pfaffian approach, s. 4
  • The rectangular lattice, s. 5
  • Rectangular lattice with a boundary vacancy, s. 7
  • The honeycomb and kagome lattices, s. 8
  • Solution of a three-dimensional dimer model, s. 8
  • Remarks, s. 9
  • References for Chapter 1, s. 9

2. The Vertex Model

  • Introduction, s. 11
  • The eight-vertex model (rectangular lattice), s. 12
  • The five-vertex model (rectangular lattice), s. 14
  • The eight-vertex model (honeycomb lattice), s. 15
  • Vertex models in higher dimensions, s. 16
  • Remarks, s. 17
  • References for Chapter 2, s. 18

3. Duality and Gauge Transformations

  • Introduction, s. 20
  • Duality relation for the Potts and the chiral Potts models, s. 20
  • Gauge transformation for the vertex model and syzygies, s. 22
  • Duality relation for frustrated spin systems, s. 23
  • Duality relation for Potts correlation functions, s. 23
  • References for Chapter 3, s. 25

4.The Ising Model

  • Introduction, s. 27
  • Ising representation of the eight-vertex model, s. 27
  • The Baxter-Wu model, s. 28
  • Density of Fisher zeroes, s. 28
  • Solution of the Ising model on nonorientable surfaces, s. 30
  • Remarks, s. 31
  • References for Chapter 4, s. 31

5. The Potts Model 

  • Introduction, s. 33
  • Graphical formulation of the Potts model, s. 34
  • Rigorous determination of the Potts critical point, s. 35
  • Potts partition function zeroes, s. 36
  • Remarks, s. 36
  • References for Chapter, s. 37

6. Critical Frontiers

  • Introduction, s. 38
  • The Potts model, s. 38
  • The antiferromagnetic Ising model in a magnetic field, s. 39
  • The Blume-Emery-Griffiths model, s. 40
  • The Ashkin-Teller model, s. 41
  • The O(n) model, s. 42
  • Remarks, s. 43
  • References for Chapter 6, s. 43

7. Percolation

  • Introduction, s. 45
  • The random-cluster model and the Potts model, s. 46
  • Percolation thresholds, s. 47
  • An infinite-range bond percolation, s. 47
  • Directed percolation, s. 47
  • Remarks, s. 48
  • References for Chapter 7, s. 49

8. Graph Theory

  • Introduction, s. 50
  • Graphical analyses in many-body theory, s. 50
  • The Potts model and the Tutte polynomial, s. 51
  • Random graphs, s. 53
  • Spanning trees, s. 53
  • Graphical analysis of lattice models, s. 54
  • References for Chapter 8, s. 55

9. Knot Invariants

  • Introduction, s. 57
  • Lattice models and knot invariants, s. 57
  • Two new knot invariants, s. 58
  • Knot invariants from spin models, s. 59
  • Bracket polynomial and the nonintersecting string model, s. 60
  • Remarks, s. 61
  • References for Chapter 9, s. 62

10. Other Topics

  • Theory of electrical circuits, s. 63
  • Quantization of the orbital angular momentum, s. 65
  • The vicious neighbor problem, s. 65
  • Restricted partitions of an integer, s. 66
  • The Hubbard model, s. 67
  • Review of a book by Ta-You Wu, s. 68
  • Eulogy on Shang-Keng Ma, s. 68
  • Professor C. N. Yang and statistical mechanics, s. 69
  • References for Chapter 10, s. 69
  • Photographs, s. 71
  • Reprinted Papers, s. 83


1. Dimer Statistics, s. 85

P1    Exactly Soluble Model of the Ferroelectric Phase Transition in Two Dimensions / F. Y. Wu, , s. 87
P2    Dimers on Two-Dimensional Lattices / F. Y. Wu, s. 90
P3    Close-Packed Dimers on Nonorientable Surfaces / W.T. Lu and F.Y. Wu, s. 105
P4    Pfaffian Solution of a Dimer-Monomer Problem:Single Monomer on the Boundary / F. Y. Wu, s. 117
P5    Remarks on the Modified Potassium Dihydrogen Phosphate Model of a Ferroelectric / F. Y. Wu, s. 121
P6    Exact Solution of Close-Packed Dimers on the Kagome Lattice / F. Wang and F. Y. Wu, s. 126
P7    Exact Solution of a Three-Dimensional Dimer System / H. Y. Huang, V. Popkov and F. Y. Wu, s. 130

2. The Vertex Model, s. 135

P8    General Lattice Model of Phase Transitions / C. Fan and F. Y. Wu, s. 139
P9    Staggered Ice-Rule Model: The Pfaffian Solution / F. Y. Wu and K. Y. Lin, s. 148
P10  Staggered Eight-Vertex Model / C. S. Hsue, K. Y. Lin and F. Y. Wu, s. 158
P11 The Odd Eight-Vertex Model / F. Y. Wu and H. Kunz, s. 167
P12  Eight-Vertex Model on the Honeycomb Lattice / F. Y. Wu, s. 179
P13  Eight-Vertex Model and Ising Model in a Non-zero Magnetic Field: Honeycomb Lattice / F. Y. Wu, s.
P14  Phase Transition in a Vertex Model in Three Dimensions / F. Y. Wu, s. 188
P15  Exact Solution of a Vertex Model in d Dimension / F. Y. Wu and H. Y. Huang, s. 192

3. Duality and Gauge Transformations, s. 201

P16  Duality Transformation in a Many-Component Spin Model / F. Y. Wu and Y. K. Wang, s. 203
P17  Duality Properties of a General Vertex Model / X. N. Wu and F. Y. Wu, s. 205
P18  Algebraic Invariants of the 0(2) Gauge Transformation / J. H. H. Perk, F. Y. Wu and X. N. Wu, s. 211
P19  The 0(3) Gauge Transformation and 3-state Vertex Models / L. H. Gwa and F. Y. Wu, s. 216
P20  Duality Relation for Frustrated Spin Models / D. H. Lee and F. Y. Wu, , s. 221
P21  Duality Relations for Potts Correlation Functions / F. Y. Wu, s. 226
P22  Sum Rule Identities and the Duality Relation for the Potts n-Point Boundary Correlation Function / F. Y. Wu and H. Y. Huang, , s. 231

4. The Ising Model, s. 235

P23  Ising Model with Four-Spin Interactions / F. Y. Wu, s. 237
P24  Exact Solution of an Ising Model with Three-spin Interactions on a Triangular Lattice / R. J. Baxter and F. Y. Wu, s. 240
P25  Density of the Fisher Zeroes for the Ising Model / W. T. Lu and F. Y. Wu, s. 244
P26  Ising Model on Nonorientable Surfaces: Exact Solution for the Mobius Strip and the Klein Bottle / W. T. Lu and F. Y. Wu, s. 262

5. The Potts Model, s. 271

P27  Equivalence of the Potts Model or Whitney Polynomial with an Ice-Type Model / R. J. Baxter, S. B. Kelland and F. Y. Wu, s. 273
P28  The Potts Model / F. Y. Wu s. 283
P29  Potts Model of Magnetism (Invited) / F. Y. Wu, s. 317
Exactly Solved Models
P30  Exact Results for the Potts Model in Two Dimensions / A. Hintermann, H. Kunz and F. Y. Wu, s. 322
P31  Partition Function Zeros of the Square Lattice Potts Model / C. N. Chen, C. K. Hu and F. Y. Wu, s. 332

6. Critical Frontiers, s. 337

P32  Critical Point of Planar Potts Models / F. Y. Wu, s. 339
P33  New Critical Frontiers for the Potts and Percolation Models / F. Y. Wu, s. 345
P34  Critical Frontier of the Antiferromagnetic Ising Model in a Magnetic Field: The Honeycomb Lattice / F. Y. Wu, X. N. Wu and H. W. J. Blote, s. 349
P35  Critical Surface of the Blume-Emery-Griffiths Model on the Honeycomb Lattice / L. H. Gwa and F. Y. Wu, s. 353
P36  Two Phase Transitions in the Ashkin-Teller Model / F. Y. Wu and K. Y. Lin, s. 356

7. Percolation, s. 361

P37  Percolation and the Potts Model / F. Y. Wu, s. 363
P38  An Infinite-Range Bond Percolation / F. Y. Wu, s. 372
P39  Domany-Kinzel Model of Directed Percolation: Formulation as a Random-Walk Problem and Some Exact Results / F. Y. Wu and H. E. Stanley, s. 373

8. Graph Theory, s. 377

P40  Cluster Development in an ./V-Body Problem / F. Y. Wu, s. 379
P41  Potts Model and Graph Theory / F. Y. Wu, s. 385
P42  On the Rooted Tutte Polynomial / F. Y. Wu, C. King and W. T. Lu, s. 399
P43  Random Graphs and Network Communication / F. Y. Wu, s. 411
P44  Spanning Trees on Hypercubic Lattices and Nonorientable Surfaces / W. J. Tzeng and F. Y. Wu, s. 415
P45  On the Triangular Potts Model with Two- and Three-Site Interactions / F. Y. Wu and K. Y. Lin, s. 422
P46  Nonintersecting String Model and Graphical Approach: Equivalence with a Potts Model / F. Y. Wu and J. H. H. Perk, s. 430

9. Knot Invariants, s. 447

P47  Knot Theory and Statistical Mechanics / F. Y. Wu, s. 449
P48  New Link Invariant from the Chiral Potts Model / F. Y. Wu, P. Pant and C. King, s. 482

10. Other Topics, s. 487

P49  Theory of Resistor Networks: The Two-Point Resistance / F. Y. Wu, s. 489
P50  On the Eigenvalues of Orbital Angular Momentum / D. M. Kaplan and F. Y. Wu, s. 510
P51  The Vicious Neighbour Problem / R. Tao and F. Y. Wu, s. 513
P52  Directed Compact Lattice Animals, Restricted Partitions of an Integer, and the Infinite-State Potts Model / F. Y. Wu, G. Rollet, H. Y. Huang, J.-M. Maillard, C. K. Hu and C. N. Chen, s. 521
P53  The Infinite-State Potts Model and Solid Partitions of an Integer / H. Y. Huang and F. Y. Wu, s. 525
P54  Absence of Mott Transition in an Exact Solution of the Short-Range, One-Band Model in One Dimension / E. H. Lieb and F. Y. Wu, s. 531
P55  The One-Dimensional Hubbard Model: A Reminiscence / E.  H. Lieb and F. Y. Wu, s. 535
P56  Book Review: Lectures on the Kinetic Theory of Gases, Non-Equilibrium Thermodynamics and Statistical Theories / A. Widom and F. Y. Wu, s. 562
P57  In Memorial of Sheng-Keng Ma / F.  Y. Wu, s. 566
P58  Professor C. N. Yang and Statistical Mechanics / F. Y. Wu, s. 569

APPENDIX, s. 581

Research Summary
A Challenge in Enumerative Combinatorics: The Graph of Contributions of Professor Fa-Yueh Wu Review of F. Y. Wu's Research by J.-M. Maillard, s. 583
Fa Yueh Wu: Vita, s. 635
Index of Names in the Commentaries, s. 639

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