Computational Studies of
Pure and Dilute Spin ModelsCopyright 2000 Peter Meyer
Contents
Abstract
Acknowledgements Chapter 1: Spin Models
1.1 The Role of Models in PhysicsChapter 2: Validation of the Simulation Program
1.2 Computational Physics
1.3 Modelling Magnetic Material
1.4 Lattice Geometries
1.5 Ising and Potts Spin Models
1.6 Dynamics and the Principle of Detailed Balance
1.7 Single Spin Flip Dynamics Algorithms
1.8 Temperature
1.9 Cluster Flip Dynamics Algorithms
1.10 Time
1.11 Boundary Conditions
1.12 Finite-Size Effects
2.1 The Simulation ProgramChapter 3: Critical Temperatures of Pure Ising Spin Models
2.2 Comparison of Results for Internal Energy and Specific Heat
with Those from High Temperature Series Expansion
2.3 Comparison of Simulation Results from Different Dynamics Algorithms
3.1 The Binder CumulantChapter 4: Critical Temperatures of Dilute Ising Spin Models.
3.2 Thermal Equilibrium
3.3 The Critical Temperatures of Three Pure 2d Lattices
3.4 The Critical Temperatures of Two Pure 3d Lattices
3.5 The Critical Temperature of the Pure 4d Hypercubic Lattice
4.1 Thermal Equilibrium in Dilute SystemsChapter 5: Extraction of the Critical Exponent of the Magnetization.
4.2 A Critical Temperature of the Ising Cubic Lattice with Site Dilution
4.3 Dependence of Critical Temperature on Site Dilution in the Ising Square Lattice
4.4 Dependence of Critical Temperature on Bond Dilution in the Ising Square Lattice
5.1 IntroductionChapter 6: Short-Time Critical Dynamics
5.2 The Ising Model on the Square Lattice
5.3 The Ising Model on the Triangular Lattice
5.4 The Ising Model on the Honeycomb Lattice
5.5 The 3-state Potts Model on the Square Lattice
6.1 IntroductionChapter 7: Summary of Results and Comparison with Published Results Chapter 8: Extensions of this Work
6.2 The Ising Model
6.3 The 3-state Potts Model
6.4 The 4-state Potts Model
8.1 Development of the Simulation Software
8.2 Simulated Annealing
Appendix 1: Calculation of the Metropolis and the Glauber Transition Probabilities
for the Ising Model and for the q-state Potts Model Appendix 2: The Random Number Generator Appendix 3: Contents of the Disk Appendix 4: The FIT Programs Appendix 5: Data Plotted in Graphs Appendix 6: Site and Bond Percolation Thresholds Appendix 7: Determination of Correlation Lengths Appendix 8: Relaxation Time and Singular Dynamic Scaling References
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