285420 Classical Statistical Models (V) (SoSe 2016)

In this lecture I will review classical statistical models. Prominent examples are spin models such as the Potts models and O(N) models; some of its duals such as solid on solid models; random walks and percolation; Hard sphere ensembles and loop gases; systems with entropic forces such as monomer-dimer models and polymer models.

These models typically capture some aspectes of marcroscopic systems in thermal equilibrium. We will focus mainly on the phases and phase transitions within these models. We will review the theory of critical phenomena and universality.

We will investigate analytic methods for low-dimensional models such as the transfer matrix method, and low and high temperature expansions.
For models in higher-dimensions we will introduce Monte Carlo techniques. I will review the properties of Markov chains and introduce some Monte Carlo algorithms used in statistical mechanics.

Requirements for participation, required level

It is recommended to have basic knowledge in statistical mechanics, as provided in the lecture Theorie 3.

Bibliography

- David P. Landau, Kurt Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press
- Werner Krauth: Statistical Mechanics: Algorithms and Computations, Oxford University Press