دانلود کتاب Frustrated Spin Systems (Third Edition)

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CONTENTS
Preface of the First Edition
Preface of the Second Edition
Preface of the Third Edition
1. Frustration — Exactly Solved Frustrated Models
1.1. Frustration: An Introduction
1.1.1. Definition
1.1.2. Non-collinear spin configurations
1.2. Frustrated Ising Spin Systems
1.3. Mapping between Ising Models and Vertex Models
1.3.1. The 16-vertex model
1.3.2. The 32-vertex model
1.3.3. Disorder solutions for 2D Ising models
1.4. Reentrance in Exactly Solved Frustrated Ising Spin Systems
1.4.1. Centered square lattice
1.4.1.1. Phase diagram
1.4.1.2. Nature of ordering and disorder solutions
1.4.2. Kagom´e lattice
1.4.2.1. Model with NN and NNN interactions
1.4.2.2. Generalized Kagom´e lattice
1.4.3. Centered honeycomb lattice
1.4.4. Periodically dilute centered square lattices
1.4.4.1. Model with three centers
1.4.4.2. Model with two adjacent centers
1.4.4.3. Model with one center
1.4.5. Random-field aspects of the models
1.5. Evidence of Partial Disorder and Reentrance in Other Frustrated Systems
1.6. Conclusion
1.7. Note Added for the Third Edition
Acknowledgments
References
2. Properties and Phase Transitions in Frustrated Ising Systems
2.1. Introduction
2.2. Frustrated Lattices
2.2.1. Antiferromagnetic triangular lattice (2D)
2.2.2. Villain lattice (2D)
2.3. Stacked Frustrated Lattices (3D)
2.4. Ising Models on Antiferromagnetic Triangular Lattice:Effect of the Ferromagnetic Next-Nearest-NeighborInteractions
2.4.1. Model S3
2.4.2. Model S2
2.4.3. Model S1
2.5. Thermal Properties of Ising Models on Stacked Antiferromagnetic Triangular Lattice
2.6. Ising Model on Stacked Antiferromagnetic Triangular Lattice with NNN Interaction
2.6.1. Mean-field analysis
2.6.2. Monte Carlo analysis in two dimensions
2.6.3. Monte Carlo analysis in three dimensions
2.6.4. New type of intermediate phase in the generalized six-state clock model
2.7. Ising Model with Large S on Antiferromagnetic Triangular Lattice
2.8. Ising Model with Infinite Spin on Antiferromagnetic Triangular Lattice
2.9. Ising-like Heisenberg Model on Antiferromagnetic Triangular Lattice
2.10. Ising Model with Infinite Spin on Stacked Antiferromagnetic Triangular Lattice
2.11. Phase Diagram in Spin Magnitude vs. Temperature for Ising Models with Spin S on Stacked Antiferromagnetic Triangular Lattice
2.12. Effect of Antiferromagnetic Interaction between Next-Nearest-Neighbor Spins in xy-Plane
2.13. Three-Dimensional Ising Paramagnet
2.14. Antiferromagnets on Corner-Sharing Lattices
2.15. Concluding Remarks
Acknowledgments
References
3. Renormalization Group Approaches to Frustrated Magnets in d = 3
3.1. Introduction
3.2. The STA Model and Generalization
3.2.1. The lattice model, its continuum limit, and its symmetries
3.2.2. The Heisenberg case
3.2.3. The XY case
3.2.4. Generalization
3.3. Experimental and Numerical Situations
3.3.1. The XY systems
3.3.1.1. The experimental situation
3.3.1.2. The numerical situation
3.3.1.3. Summary
3.3.2. The Heisenberg systems
3.3.2.1. The experimental situation
3.3.2.2. The numerical situation
3.3.2.3. Summary
3.3.3. The N = 6 STA
3.3.4. Summary
3.4. A Brief Chronological Survey of the Theoretical Approaches
3.5. The Perturbative Situation
3.5.1. The Nonlinear Sigma (NLσ) model approach
3.5.2. The Ginzburg–Landau–Wilson model approach
3.5.2.1. The RG flow
3.5.2.2. The three- and five-loop results in d = 4− 
3.5.2.3. The improved three- and five-loop results
3.5.2.4. The three-loop results in d = 3
3.5.2.5. The large-N results
3.5.2.6. The six-loop results in d = 3
3.5.3. The six-loop results in d = 3 re-examined
3.5.3.1. Summary
3.6. The Effective Average Action Method
3.6.1. The effective average action equation
3.6.2. Properties
3.6.3. Truncations
3.6.4. Principle of the calculation
3.6.5. The O(N) × O(2) model
3.6.5.1. The flow equations
3.6.6. Tests of the method and first results
3.6.7. The physics in d = 3 according to the NPRG approach
3.6.7.1. The physics in d = 3 just below Nc(d): Scaling with a pseudo-fixed point and minimum of the flow
3.6.7.2. Scaling with or without pseudo-fixed point: The Heisenberg and XY cases
3.6.7.3. The integration of the RG flow
3.6.7.4. The Heisenberg case
3.6.7.5. The XY case
3.6.8. Summary
3.7. Conclusion and Prospects
3.8. Note Added in the Second Edition
3.9. Note Added by the Editor for the Third Edition
Acknowledgments
References
4. Phase Transitions in Frustrated Vector Spin Systems: Numerical Studies
4.1. Introduction
4.2. Breakdown of Symmetry
4.2.1. Symmetry in the high-temperature region
4.2.2. Breakdown of symmetry for ferromagnetic systems
4.2.3. Breakdown of symmetry for frustrated systems
4.2.3.1. Stacked triangular antiferromagnetic lattices
4.2.3.2. BCT Helimagnets
4.2.3.3. Stacked J1–J2 square lattices
4.2.3.4. The simple cubic J1–J2 lattice
4.2.3.5. J1–J2–J3 lattice
4.2.3.6. Villain lattice and fully frustrated simple cubic lattice
4.2.3.7. Face-centered cubic lattice
4.2.3.8. Hexagonal-close-packed lattice (hcp)
4.2.3.9. Pyrochlores
4.2.3.10. Other lattices
4.2.3.11. STAR lattices
4.2.3.12. Dihedral lattices VN,2
4.2.3.13. Right-handed trihedral lattices V3,3
4.2.3.14. P-hedral lattices VN,P
4.2.3.15. Ising and Potts-VN,1 model
4.2.3.16. Ising and Potts-VN,2 model
4.2.3.17. Landau–Ginzburg model
4.2.3.18. Cubic term in Hamiltonian
4.2.3.19. Summary
4.3. Phase Transitions between Two and Four Dimensions: 2 < d ≤ 4
4.3.1. O(N)/O(N − 2) breakdown of symmetry
4.3.1.1. Fixed points
4.3.1.2. MCRG and first-order transition
4.3.1.3. Complex fixed point or minimum in the flow
4.3.1.4. Experiment
4.3.1.5. Value of Nc
4.3.1.6. Phase diagram (N,d)
4.3.1.7. Renormalization group expansions
4.3.1.8. Short historical review
4.3.1.9. Relations with the Potts model
4.3.2. O(N)/O(N − P) breakdown of symmetry for d = 3
4.3.3. Z2 ⊗ SO(N)/SO(N − 1) breakdown of symmetry for d = 3
4.3.4. Z3 ⊗ SO(N)/SO(N − 1) breakdown of symmetry for d = 3
4.3.5. Zq ⊗ O(N)/O(N − 2) and other breakdown of symmetry in d = 3
4.4. Summary
4.5. O(N) Frustrated Vector Spins in d = 2
4.5.1. Introduction
4.5.2. Non-frustrated XY spin systems
4.5.3. Frustrated XY spin systems: Z2 ⊗ SO(2)
4.5.4. Frustrated XY spin systems: Z3 ⊗ SO(2)
4.5.5. Frustrated XY spin systems: Z2 ⊗ Z2 ⊗ SO(2) and Z3 ⊗ Z2 ⊗ SO(2)
4.5.6. Frustrated Heisenberg spin systems: SO(3)
4.5.7. Frustrated Heisenberg spin systems: Z2 ⊗ SO(3), Z3 ⊗ SO(3), . . .
4.5.8. Topological defects for N ≥ 4
4.6. Conclusions
4.7. Note Added for the Second Edition
Appendix A: Monte Carlo Simulation
A.1. Markov chains and algorithms
A.2. The histogram method
A.3. Nature of the transition
A.4. Second-order phase transition
A.5. Kosterlitz–Thouless (KT) transition
Appendix B: Renormalization Group: Landau–Ginzburg Theory, Expansions in Fixed Dimension d = 3 and for d = 4−  and its Implications for Experiments
Nomenclature
Acknowledgments
References
5. Two-Dimensional Quantum Antiferromagnets
5.1. Introduction
5.2. J1–J2 Model on the Square Lattice
5.2.1. Classical ground state and spin wave analysis
5.2.2. Order by disorder (J2 > J1/2)
5.2.3. Non-magnetic region (J2  J1/2)
5.2.3.1. Series expansions
5.2.3.2. Exact diagonalizations
5.2.3.3. Quantum Monte Carlo
5.3. Valence Bond Crystals
5.3.1. Definitions
5.3.2. One-dimensional and quasi- one-dimensional examples (spin-1/2 systems)
5.3.3. Valence Bond Solids
5.3.4. Two-dimensional examples of VBC
5.3.4.1. Without spontaneous lattice symmetry breaking
5.3.4.2. With spontaneous lattice symmetry breaking
5.3.5. Methods
5.3.6. Summary of the properties of VBC phases
5.4. Large-N Methods
5.4.1. Bond variables
5.4.2. SU(N)
5.4.3. Sp(N)
5.4.3.1. Gauge invariance
5.4.3.2. Mean-field (N = ∞ limit)
5.4.3.3. Fluctuations about the mean-field solution
5.4.3.4. Topological effects — instantons and spontaneous dimerization
5.4.3.5. Deconfined phases
5.5. Quantum Dimer Models
5.5.1. Hamiltonian
5.5.2. Relation with spin-1/2 models
5.5.3. Square lattice
5.5.3.1. Transition graphs and topological sectors
5.5.3.2. Staggered VBC for V/J > 1
5.5.3.3. Columnar crystal for V <0
5.5.3.4. Plaquette phase
5.5.3.5. Rokhsar–Kivelson point
5.5.4. Hexagonal lattice
5.5.5. Triangular lattice
5.5.5.1. RVB liquid at the RK point
5.5.5.2. Topological order
5.5.6. Solvable QDM on the kagome lattice
5.5.6.1. Hamiltonian
5.5.6.2. RK ground state
5.5.6.3. Ising pseudo-spin variables
5.5.6.4. Dimer–dimer correlations
5.5.6.5. Visons excitations
5.5.6.6. Spinons deconfinement
5.5.6.7. Z2 gauge theory
5.5.7. A QDM with an extensive ground-state entropy
5.6. Multiple-Spin Exchange Models
5.6.1. Physical realizations of multiple-spin interactions
5.6.1.1. Nuclear magnetism of solid 3He
5.6.1.2. Wigner crystal
5.6.1.3. Cuprates
5.6.2. Two-leg ladders
5.6.3. MSE model on the square lattice
5.6.4. RVB phase of the triangular J2–J4 MSE
5.6.4.1. Non-planar classical ground states
5.6.4.2. Absence of N´eel LRO
5.6.4.3. Local singlet–singlet correlations — Absence of lattice symmetry breaking
5.6.4.4. Topological degeneracy and Lieb–Schultz–Mattis theorem
5.6.4.5. Deconfined spinons
5.6.5. Other models with MSE interactions
5.7. Antiferromagnets on the Kagome Lattice
5.7.1. Ising model
5.7.2. Classical Heisenberg models on the kagome lattice
5.7.3. Nearest-neighbor RVB description of the spin-1/2 kagom´e antiferromagnet
5.7.4. Spin-1/2 Heisenberg model on the kagom´e lattice: numerics
5.7.4.1. Ground-state energy per spin
5.7.4.2. Correlations
5.7.4.3. Spin gap
5.7.4.4. Singlet gap
5.7.4.5. Entanglement entropy and signature of a Z2 liquid
5.7.4.6. Spin liquids on the kagom´e lattice and projective symmetry groups
5.7.5. Competing phases
5.7.5.1. Valence bond crystals
5.7.5.2. U(1) Dirac spin liquid
5.7.5.3. Spontaneously breaking the time-reversal symmetry, “chiral” spin liquids
5.7.6. Experiments in compounds with kagom´e-like lattices
5.8. Conclusions
References
6. One-Dimensional Quantum Spin Liquids
6.1. Introduction
6.2. Unfrustrated Spin Chains
6.2.1. Spin-1/2 Heisenberg chain
6.2.2. Haldane’s conjecture
6.2.3. Haldane spin liquid: Spin-1 Heisenberg chain
6.2.4. General spin-S case
6.2.5. Two-leg spin ladder
6.2.6. Non-Haldane spin liquid
6.3. Frustration Effects
6.3.1. Semi-classical analysis
6.3.2. Spin liquid phase with massive deconfined spinons
6.3.3. Field theory of spin liquid with incommensurate correlations
6.3.4. Extended criticality stabilized by frustration
6.3.4.1. Critical phases with SU(N) quantum criticality
6.3.4.2. Chirally stabilized critical spin liquid
6.4. Concluding Remarks
6.5. Note Added for the Second Edition
Acknowledgments
References
7. Spin Ice
7.1. Introduction
7.2. From Water Ice to Spin Ice
7.2.1. Pauling’s model
7.2.2. Why is the zero-point entropy not zero?
7.2.3. Generalizations of Pauling’s model
7.2.3.1. Wannier’s model
7.2.3.2. Anderson’s model
7.2.3.3. Vertex models
7.2.3.4. Possibility of realizing magnetic vertex models
7.2.4. Spin ice
7.2.4.1. Definition of the spin ice model and its application to Ho2Ti2O7
7.2.4.2. Identification of spin ice materials
7.2.4.3. Basic properties of the spin ice materials
7.2.5. Spin ice as a frustrated magnet
7.2.5.1. Frustration and underconstraining
7.2.5.2. 111 Pyrochlore models
7.3. Properties of the Zero-Field Spin Ice State
7.3.1. Experimental properties
7.3.1.1. Heat capacity: Zero-point entropy
7.3.1.2. Low field magnetic susceptibility: Spin freezing
7.3.1.3. Spin arrangement observed by neutron scattering
7.3.2. Microscopic theories and experimental tests
7.3.2.1. Near-neighbor spin ice model: Successes and failures
7.3.2.2. The problem of treating the dipolar interaction
7.3.2.3. The Ewald Monte Carlo
7.3.2.4. Mean-field theory
7.3.2.5. The loop Monte Carlo
7.3.2.6. Application of the dipolar model to neutron scattering results
7.3.2.7. How realistic is the dipolar model?
7.4. Field-Induced Phases
7.4.1. Theory
7.4.1.1. Near-neighbor model
7.4.1.2. Dipolar model
7.4.2. Magnetization measurements above T = 1K
7.4.3. Bulk measurements at low temperature
7.4.3.1. [111] Direction
7.4.3.2. [110] Direction
7.4.3.3. [100] Direction
7.4.3.4. [211] Direction
7.4.3.5. Powder measurements
7.4.4. Neutron scattering results
7.4.4.1. [110] Direction
7.4.4.2. [100], [111], and [211] directions
7.4.5. Kagom´e ice
7.4.5.1. Basic kagom´e ice model and mappings
7.4.5.2. Experimental results: Specific heat
7.4.5.3. Theory of the kagom´e ice state: Kastelyn transition
7.5. Spin Dynamics of the Spin Ice Materials
7.5.1. Experimental quantities of interest
7.5.1.1. Correlation functions and neutron scattering
7.5.1.2. Fluctuation–dissipation theorem and AC susceptibility
7.5.1.3. Spectral shape function
7.5.1.4. Exponential relaxation
7.5.2. Differences between Ho2Ti2O7 and Dy2Ti2O7
7.5.3. Relaxation at high temperature, T ∼ 15K and above
7.5.3.1. AC susceptibility (AC-χ)
7.5.3.2. Neutron spin echo (NSE)
7.5.3.3. Origin of the 15K AC susceptibility peak
7.5.4. Relaxation in the range 1K ≤ T ≤ 15K
7.5.4.1. AC susceptibility: Phenomenological model
7.5.4.2. AC susceptibility: Toward a microscopic model
7.5.5. Spin dynamics in the spin ice regime below 1K
7.5.5.1. Slow relaxation
7.5.5.2. Evidence for residual dynamics in the frozen state
7.5.6. Doped spin ice
7.5.7. Spin ice under pressure
7.6. Spin Ice-Related Materials
7.6.1. Rare earth titanates
7.6.2. Other pyrochlores related to spin ice
7.7. Conclusions
7.8. Note Added for the Second Edition
Acknowledgments
References
8. Experimental Studies of Frustrated Pyrochlore Antiferromagnets
8.1. Introduction
8.2. Pyrochlore Lattices
8.3. Neutron Scattering Techniques
8.4. Cooperative Paramagnetism in Tb2Ti2O7
8.5. The Spin Glass Ground State in Y2Mo2O7
8.6. Composite Spin Degrees of Freedom and Spin-Peierls-Like Ground State in the Frustrated Spinel ZnCr2O4
8.7. Conclusions and Outlook
Acknowledgments
References
9. Recent Progress in Spin Glasses
9.1. Two Pictures
9.1.1. Mean-field picture
9.1.2. Droplet picture
9.2. Equilibrium Properties of 2D Ising Spin Glasses
9.2.1. Zero-temperature transition?
9.2.2. Droplet argument for Gaussian-coupling models
9.2.3. Droplets in Gaussian-coupling models: Numerics
9.2.4. Finite-temperature transition?
9.3. Equilibrium Properties of Three-Dimensional Models
9.3.1. Finite-temperature transition?
9.3.2. Universality class
9.3.3. Low-temperature phase of the ±J model
9.3.4. Low-temperature phase of the Gaussian-coupling model
9.3.5. Effect of magnetic fields
9.3.6. Sponge-like excitations
9.3.7. TNT picture — introduction of a new scaling length
9.3.8. Arguments supporting the droplet picture
9.4. Models in Four or Higher Dimensions
9.5. Aging
9.5.1. A growing length scale during aging?
9.5.2. Two time quantities: Isothermal aging
9.5.3. More complicated temperature protocols
9.5.4. Violation of the fluctuation–dissipation theorem
9.5.5. Hysteresis in spin glasses
9.6. Equilibrium Properties of Classical XY and Heisenberg Spin Glasses
9.6.1. Continuous spin models in three dimensions
9.6.2. Continuous spin models in higher dimensions
9.6.3. Potts spin glasses
9.7. Weak Disorder
9.7.1. Phase diagram of the discrete spin models
9.7.2. Dynamical properties
9.7.3. The renormalization group approach for the discrete models
9.7.4. The location of the multi-critical point
9.7.5. Phase diagram of the random XY model in two dimensions
9.8. Quantum Spin Glasses
9.8.1. Random transverse Ising models
9.8.2. Mean-field theory
9.8.3. Mean-field theory — Dissipative effects
9.8.4. Mean-field theory — Dynamics
9.8.5. Heisenberg quantum spin glasses
9.8.5.1. Finite dimensions
9.8.5.2. Mean-field model
9.9. Conclusions and Remaining Problems
Acknowledgments
References
10. Frustrated Magnetic Thin Films: Spin Waves and Skyrmions
10.1. Introduction
10.2. Surface Effects in Helimagnets
10.2.1. Introduction
10.2.2. Model and classical ground state
10.2.3. Green’s function method
10.2.4. General formulation for non-collinear magnets
10.2.5. BCC helimagnetic films
10.2.6. Results from the Green’s function method
10.2.7. Spectrum
10.2.8. Spin length at T = 0 — Transition temperature
10.2.9. Layer magnetizations
10.2.10. Effect of anisotropy and surface parameters
10.2.11. Effect of the film thickness
10.2.12. Classical helimagnetic films: Monte Carlo simulation
10.2.13. Summary
10.3. Dzyaloshinskii–Moriya (DM) Interaction in Thin Films: Spin Waves
10.3.1. Introduction
10.3.2. Model and ground state
10.3.3. Results from Green’s function method
10.3.4. Two dimensions: Spin wave spectrum and magnetization
10.3.5. The case of thin films: Spin wave spectrum, layer magnetizations
10.3.6. Discussion
10.3.7. Summary
10.4. Stability and Phase Transition of Skyrmion Crystals Generated by DM Interaction
10.4.1. Introduction
10.4.2. Model and ground state
10.4.3. Stability of Skyrmion crystal at finite temperatures
10.4.4. Summary
10.5. Elastic Effects in Membranes with DM Interaction
10.5.1. Triangulated lattices and skyrmion model
10.5.1.1. Triangulated lattices
10.5.1.2. Skyrmion model
10.5.1.3. Frame tension
10.5.1.4. Monte Carlo technique
10.5.2. Results under isotropic strain
10.5.2.1. Phase diagram and snapshots
10.5.2.2. Frame tension and interaction energies
10.5.3. Results under uniaxial strains
10.5.4. Conclusions
Acknowledgments
References