Phase transitions course

Phase transitions are ubiquitous in Nature. We are all familiar with the different phases of water (vapour, liquid and ice), and with the change from one to the other. Changes of phase are called phase transitions. These phenomena are very important not only in natural processes, but also in industry. To name just a few everyday examples: the evaporation of liquids, formation of ice or liquid water sheets on surfaces, construction of different materials in metallurgy...

Here we give an elemantary introduction to the sub ject of phase transitions. This is a vast subject, and a lot of research effort is still being dedicated to phase transitions, both from experimental and theoretical points of view. The first microscopically-based understanding of phase transitions is due to van der Waals, who in 1873 presented a primitive theory of the gas-liquid transition. In his doctoral thesis he presented the van der Waals equation of state, and linked its parameters to a molecular model. Even though it was a first attempt, it laid down the basic ideas on which the modern theoretical understanding is based. Later, Landau (1937) proposed a phenomenological (not fully microscopic) approach that was crucial to understand second-order phase transitions and later developments. Another paramount step forward was given by Wilson (1971) and others, who developed a powerful and unifying set of concepts (basically the idea of scaling close to critical points and the renormalisation group) for second-order phase transitions.

First-order transitions are less well understood, and current work relies almost exclusively on mean-field theory, which we shall review and apply in various contexts.

To download clik on the link below :