The KTHNY theory

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Table of contents

General introduction
I Two-dimensional melting
Introduction
1 Transitions in two dimensions
1.1 Two-dimensional solids
1.2 Transitions in 2D XY models
1.3 Scenarios for two-dimensional melting
2 Event-chain Monte Carlo algorithms for hard spheres
2.1 Hard-sphere simulations
2.2 The event-chain algorithm
2.3 Implementation of the algorithm
3 Simulation method
3.1 Choice of ensemble
3.2 Statistical errors
3.3 Computation of observables
4 Hard-disk melting transition
4.1 Phase coexistence
4.2 Nature of the phases
4.3 Thermalization and finite-size effects
4.4 Other simulations
Conclusion
II Perfect sampling
Introduction
5 The coupling-from-the-past method
5.1 The Monte Carlo method
5.2 Coupling from the past
5.3 Survey problem
6 Damage spreading and coupling in Markov chains
6.1 Chaos in Markov chains
6.2 Spin glass
6.3 Hard spheres
6.4 Griffeath’s coupling
Conclusion
7 Publications
7.1 Publication I
7.2 Publication II
7.3 Publication III