Spin glasses

Abstract

[en] At the beginning of the 70s, last century, physician scientists started to study, inside the studies about the state of matter, some mathematical structures called spin glasses. After that, and due to the need to go deeper in the knowledge of the study of the properties of these structures, mathematicians started to study them as well in order to understand their properties from a less physical point of view. In this paper we present an introduction to three of the easiest models of spin glasses. In chapter one we will introduce spin glasses, and we will see an example which will help us to understand better this concept. We will also introduce the basic concepts which we will use along this paper, such as free energy and the Gibbs’ measure. We will use the next chapters to study several easy models of spin glasses. In chapter two we will study model REM, which is possibly one of the existing easiest models. Chapters three and four contain details about Sherrington and Kirkpatrick models, with and without external field respectively. In chapter four we will also see how the action of a magnetic field is modelled in this kind of structures, and we will obtain different results in both models.