The thermodynamic properties of the mean spherical model of ferromagnetism, in the Curie-Weiss version, with interactions between all pairs of spin variables, can be exactly calculated and analyzed in a particularly simple and pedagogical fashion. It is then interesting to consider a quantum version of this model, which we call "elementary quantum spherical model", and which can also be analyzed in detail, in terms of the temperature T and of a parameter g associated with the quantum fluctuations. This system provides one the simplest examples of a quantum phase transition. In a pedagogical fashion, we make contact with several results from the literature, and present a number of comments on some questions, as the correction of anomalies in the classical behavior and the role of the thermodynamic limit in the onset of a "Bose-Einstein singularity".
spherical model; quantum spherical model; phase transitions
