Physics of Phase Transitions

We learned in school that matter exists in three forms: solid, liquid and gas, as well as other more subtle things such as the fact that 'evaporation produces cold. ' The science of the states of matter was born in the 19th century. It has now grown enormously in two directions: 1) The transitions have multiplied: first between a solid and a solid, par- ticularly for metallurgists. Then for magnetism, illustrated in France by Louis Neel, and ferro electricity. In addition, the extraordinary phenomenon of su- perconductivity in certain metals appeared at the beginning of the 20th cen- tury. And other superfluids were recognized later: helium 4, helium 3, the matter constituting atomic nuclei and neutron stars . . . There is now a real zoology of transitions, but we know how to classify them based on Landau's superb idea. 2) Our profound view of the mechanisms has evolved: in particular, the very universal properties of fluctuations near a critical point - described by Kadanoff's qualitative analysis and specified by an extraordinary theoretical tool: the renormalization group. Without exaggerating, we can say that our view of condensed matter has undergone two revolutions in the 20th century: first, the introduction of quantum physics in 1930, then the recognition of 'self-similar' structures and the resulting scaling laws around 1970. .