**2D Ising model**- Phase transitions in magnetics

Magnetics. Magnetization and interaction energy. The Boltzmann distribution. Entropy. - The Monte-Carlo method

Markov random walks. Importance sampling. The Metropolis algorithm. Detailed balance conditions. Susceptibility and specific heat. The thermostat algorithm. High non-equilibrium spin flip dynamics. - Critical slowing down

Relaxation time of magnetization. Critical slowing down. - Ferromagnetic phase transition

Second order phase transition. Critical exponents of the 2D Ising model. - Antiferromagnetics

Order parameter in antiferromagnetics. Frustrations.

- Phase transitions in magnetics
**Topological exitations in ferromagnetics**- Vortices in the XY model

Vortices and antivortices. Birth and annihilation of the vortex - antivortex pair. The Kosterlitz and Thouless phase transiton. 3D vortex threads and rings. - Excitations in 1D spin chain

Energy of spin chain. Topological charge. Maps of circle. Continuum limit. - Topological solitons in the Heisenberg ferromagnetic

Instantons and anti-instantons. Maps of sphere. What does hedgehog hide? - Hedgehog zoo

- Vortices in the XY model
**Percolation**- Geometric phase transition

2D site percolation. Cluster labeling. Phase transition. Single 2D and 3D clusters. - Percolation characteristic functions

The cluster-size distribution. Characteristic functions. - Continuum percolation

2D electron gas conductivity. Percolation in random potential landscape. Anderson localization. Electron localization in high magnetic field. "Shoreline" percolation. - White, correlated and fractal noise
- Critical exponents of characteristic functions

Universal percolating claster. Critical exponents.

- Geometric phase transition
**Path integrals in Quantum mechanics****WebCL and simulations on GPU**- Ising model
- Vortices in the XY model
- n-field

1. *Harvey Gould, Jan Tobochnik*
Introduction to Computer Simulation Methods:
Applications to Physical Systems

2. Monte-Carlo methods in Statistical Physics (edited by *K.Binder*)

E-notes 2D Ising model free sources the whole perc.zip (240kb 14 June 04)