Spin glasses

Abstract

In the last century, the aggregation states of matter have been one of the most important aspects studied by physicists: the Spin Glass is one of those states. The main objective of this TFG is to study the Spin Glass behavior presented in some materials introducing several models and mathematical concepts, as well as some important applications in other disciplines such as biology, mathematical optimization and neural networks. The models studied more deeply in this document are the REM (Random Energy Model) and the Sherrington-Kirkpatrick model. These are called models on average, i.e. all the spins in the system interact somehow between them. The real models are so complex that, nowadays, there are still many issues to resolve. The REM is a ”toy model” and studied their behavior is helpful to understand basic concepts of statistical mechanics of disordered systems. The Sherrington-Kirkpatrick model is more interesting than REM because their behavior is useful in fields such as computing or optimization. Finally, the presentation of the Sherrington-Kirkpatrick model affected by an external magnetic field is basically to introduce the Cavity Method and the Smart Path Method.