The wrapping probabilities

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Table of contents

I Coarsening and percolation in 2d kinetic Ising models
1 Percolation in the 2d KIM evolving under Glauber dynamics
1.1 Introduction
1.2 Definition of the KIM equipped with Glauber dynamics
1.3 Observables
1.4 Percolation phenomena
1.4.1 Snapshots
1.4.2 Largest cluster
1.4.3 Pair connectedness function
1.5 Detailed numerical analysis
1.5.1 Growing length
1.5.2 Wrapping probabilities
1.5.3 Averaged squared winding angle
1.5.4 Largest cluster scaling
1.5.5 Number density of domain areas
1.6 Conclusions
2 Coarsening and percolation in the 2d KIM evolving with COP dynamics
2.1 Introduction
2.2 Definition of the model
2.3 Kawasaki dynamics
2.3.1 Snapshots
2.4 Numerical analysis
2.4.1 The excess-energy growing length
2.4.2 Wrapping probabilities
2.4.3 Average squared winding angle
2.4.4 Largest cluster scaling
2.4.5 Pair connectedness function
2.4.6 Number density of domain areas
2.5 Conclusions
3 Coarsening in the 2d Voter Model: hints of a new criticality
3.1 Introduction
3.2 Definition of the Model
3.3 Numerical analysis
3.3.1 Average squared winding angle
3.3.2 Wrapping probabilities
3.3.3 Largest cluster scaling
3.3.4 Number density of domain areas
3.4 Conclusions
II Quench dynamics of the isolated p = 2 spherical spin glass model
4 Quench dynamics of the isolated p = 2 spherical spin glass model
4.1 Introduction
4.2 Background
4.2.1 Definition of the model
4.2.2 The potential energy landscape
4.2.3 The equilibrium behaviour
4.2.4 Relaxation dynamics
4.3 Dynamics of the isolated system after a quench of the disorder strength
4.3.1 Energy change
4.3.2 Asymptotic analysis
4.4 Dynamics of the finite-size system
4.4.1 Formal solution of the mode dynamics
4.4.2 Initial conditions: equilibrium averages for finite N
4.4.3 Behaviour under stationary conditions
4.5 Numerical results
4.5.1 The phase diagram
4.5.2 Constant energy dynamics
4.5.3 Quench dynamics
4.6 Integrals of motion
4.6.1 Gibbs-Boltzmann equilibrium assumption
4.6.2 Fluctuations of the integrals of motion in the equal energy hypersurface
4.7 Conclusions
Appendices
Appendix A 
A.1 Finite-temperature effects for KIM evolving with Glauber dynamics
A.2 Ising model evolving with Glauber dynamics on a honeycomb lattice
A.2.1 Percolation phenomena
Appendix B 
B.1 Ising model evolving with nonlocal Kawasaki dynamics
B.1.1 The growing length
B.1.2 Critical percolation phenomena
B.1.3 Summary
Appendix C 
C.1 Generalized 2d KIM
C.2 Some analytic results for the voter model
Appendix D 
D.1 Equilibrium measure for the simple harmonic oscillator after a quench
D.2 Neumann’s model, integrability and equilibration
Bibliography