Numerical methods in Glassy systems

In these lectures I describe some theoretical tools and numerical techniques to investigate glassy systems. The discussion is centered on spin glasses where there has been a large amount of theoretical as well as numerical work during the recent years. After discussing the utility of introducing real replicas in numerical simulations, I analyze topics such as equilibration methods and the analysis of the critical point. Improved Monte Carlo methods like simulated tempering and parallel tempering are also discussed. 1 Introduction The reliability of numerical simulations to successfully investigate glassy behavior is an open problem in modern statistical physics. To numerically investigate equilibrium properties in real glassy systems we face very hard problems related to the existence of relaxation processes with very long time scales. Indeed, the main problem which distinguishes glasses from usual systems (for instance, ferromagnets, liquids, gases,...) is the impossibility to rea..