Magnetic Systems With Competing Interactions

✍ Scribed by H. T. Diep

• Publisher: World Scientific Pub Co Inc
• Year: 1994
• Tongue: English
• Leaves: 351
• Category: Library

✦ Synopsis

This text covers mainly frustrated spin systems with possible applications in domains where physical systems can be mapped into the spin language. It is suitable for students and researchers in statistical physics, magnetism and material sciences.

✦ Table of Contents

CONTENTS......Page 10
PREFACE......Page 6
1. Introduction......Page 16
2. Various models and predictions......Page 19
2.1. Triangular lattices and helical spin structures......Page 20
2.2. Fcc, hcp and rhombohedral antiferromagnets: order by disorder......Page 24
2.3. Kagome and pyrochlore antiferromagnets: more disorder......Page 26
3. Mean-field Landau models and Monte Carlo simulations......Page 28
3.1. Phenomenological Landau-type free energy......Page 29
3.2. Mean-field derivation of a Landau free energy......Page 32
3.3. Monte Carlo simulations......Page 34
4. Simple hexagonal antiferromagnet: magnetic phase diagrams and multicritical points......Page 38
4.1. Planar model with antiferromagnetic interlayer coupling......Page 40
4.2. Planar model with ferromagnetic interlayer coupling......Page 46
4.3. Heisenberg model with axial anisotropy......Page 50
4.4. Next-nearest-neighbor interactions......Page 54
5. Other problems of interest......Page 56
6. Concluding remarks......Page 58
8. References......Page 60
1. Introduction......Page 66
2. Effective action for frustrated models......Page 69
2.1. Non frustrated Heisenberg models.......Page 70
2.2. Frustrated Heisenberg models......Page 72
2.2.1. The Non Linear Sigma model......Page 76
2.2.2. The Landau-Ginzburg-Wilson models......Page 77
2.2.3. The large-N approaches......Page 79
2.3. The Stacked Triangular Heisenberg Antiferromagnet......Page 80
3. The Landau-Ginzburg-Wilson models: Renormalization......Page 83
3.1. The two vector model......Page 84
3.2. The three vector model......Page 88
3.3. Concluding remarks......Page 90
4.1. Renormalization of the NLcr model in D = 2 + e......Page 91
4.2. The S0(3) model......Page 93
4.2.1. The coupling constant renormalization......Page 95
4.2.2. The field renormalization......Page 96
4.2.3. The renormalization group equations......Page 98
4.3. O(N) ® O(2)/O(N - 2) ® O(2) models and two loop results......Page 100
5. Interpolating between D = 2 + ε and D = 4 - ε......Page 103
6. Frustrated models in two dimensions......Page 107
6.1. The correlation length......Page 109
6.2. The spin stiffness......Page 111
6.2.1. The effective O(3) ® O(2)/O(2) spin stiffness tensor......Page 113
7. Quantum frustrated spin systems in two dimensions.......Page 114
7.1. Effective theory for quantum frustrated antiferromagnets......Page 117
7.2. The quantum top model......Page 118
7.3. The quantum phase transition......Page 120
7.4. Spontaneous symmetry breaking and the tower of states......Page 123
7.5. Finite temperature properties.......Page 126
7.6. Concluding remarks......Page 130
8. Conclusion......Page 131
10. References......Page 132
1. Introduction......Page 135
2. One—Dimensional Models......Page 138
3. Two Dimensions and Finite—Size Scaling Analysis......Page 142
3.1. Finite-Size Scaling Analysis of the Small-J2 Antiferromagnetic Phase......Page 146
3.2. Finite-Size Scaling Analysis of the Large-J2 Antiferromagnetic Phase......Page 156
3.3. The Nature of the Intermediate Phase......Page 159
4. Frustration in Triangular Lattice Systems......Page 171
6. References......Page 173
1. Introduction......Page 176
2.1. The 16-vertex model......Page 178
2.2. The 32-vertex model......Page 180
2.3. Disorder solutions for two-dimensional Ising models......Page 190
3. Reentrance in exactly solved frustrated Ising spin systems......Page 192
3.1. Centered square lattice......Page 193
3.1.2. Nature of ordering and disorder solutions......Page 194
3.2.1. Model with nn and nnn interactions......Page 196
3.2.2. Generalized Kagome lattice......Page 197
3.3. Centered honeycomb lattice......Page 202
3.4. Periodically dilute centered square lattices......Page 205
3.4.1. Model with three centers (Fig. 25a)......Page 208
3.4.2. Model with two adjacent centers (Fig. 25b)......Page 210
3.4.3. Model with one center (Fig. 25d)......Page 211
4. Conclusion......Page 213
6. References......Page 215
1. Introduction......Page 217
2. Ising model on two-dimensional frustrated lattice and on stacked frustrated lattice......Page 220
3. Ising model on antiferromagnetic triangular lattice: Effect of ferromagnetic next-nearest-neighbor interaction......Page 222
4. Ising model on stacked antiferromagnetic triangular lattice......Page 228
5. Ising model with infinite-spin on antiferromagnetic triangular lattice......Page 230
6. Ising model with infinite-spin on stacked antiferromagnetic triangular lattice......Page 236
7. Phase diagram in spin-magnitude versus temperature for Ising models with spin S on stacked antiferromagnetic triangular lattice......Page 239
8. Effect of antiferxomagnetic interaction between next-nearest-neighbor spins in xy-plane......Page 242
9. Three-dimensional, Ising paramagnet......Page 246
10. Concluding remarks......Page 250
12. References......Page 251
1. Introduction......Page 253
2.1. Magnetization Measurements......Page 255
3. Mean-Field Theory of Spin......Page 258
4.1. Methods......Page 261
• Monte CarJo Method......Page 262
• Defect-wall energy method......Page 263
• Migdal-Kadanoff renormalization-group method......Page 264
4.2. Spin Hamiltonians and Effects 0} Randomness......Page 265
4.3. Edwards-Anderson Model......Page 266
4.4. Ising Models......Page 267
4.5. N- Component Vector Models......Page 268
5. "Recent" Experimental Investigations of Reentrant Spin Glasses......Page 275
5.1. Neutron Depolarization Experiments......Page 276
5.2. Neutron Scattering Experiments......Page 278
5.3. Mossbauer Spectroscopy......Page 281
5.4. Muon Spin Resonance Experiments......Page 282
5.5. Lorentz Electron Microscopy......Page 283
5.6. Hysteresis and Influence of Anisotropy......Page 284
5.7. Discussion......Page 286
6.1. Nishimori Line and Phase Diagram of Gauge Glasses......Page 287
8. Acknowledgments......Page 293
9. References......Page 294
1. Introduction......Page 301
2.1. Critical Phenomena......Page 302
2.2. Experimental Considerations......Page 304
3. Stacked Triangular-Lattice (STL) Antiferromagnets......Page 309
4. CsMnBr3 : an XY STL Antiferromagnet......Page 311
4.1. Measurements in Zero Magnetic Field......Page 312
4.2. Measurements in a Magnetic Field......Page 317
4.3. Exponent Estimates: Kawamura vs. Azaria et al.......Page 322
5. The Helical Rare-Earth Metals: Ho, Dy, and Tb......Page 323
6.1. Theoretical Models......Page 327
6.2. Experimental Studies of CsCoBr3 and CsCoCl3......Page 328
6.3. The Role of Solitons in the Formation of the Ordered State in CsCoBr3......Page 330
7. Antiferromagnetism on a Network of Corner-Sharing Tetrahedra......Page 333
7.1. The Pyrochlores......Page 334
7.2. Neutron-Scattering Studies of Tb2Mo2Oi......Page 335
7.3. Experimental Studies of Other Pyrochlores......Page 338
8. Concluding Remarks......Page 340
10. References......Page 341
INDEX......Page 346