The problem of phase transitions in statistical mechanics

Abstract

The first part of this review deals with the one-phase approach to the statistical theory of phase transitions. This approach is based on the assumption that a phase transition of the first kind is due to the loss of stability by the host phase. We demonstrate that it is practically impossible to find the coordinates of the points of phase transition using this criterion in the framework of the global Gibbs theory which describes the state of the entire macroscopic system. On the basis of Ornstein-Zernicke equation we formulate the local approach that analyzes the state of matter inside the correlation sphere of radius Rc ≈ 10Å. This approach is proved to be as rigorous as the Gibbs theory. In the context of the local approach we formulate the criterion that allows finding the points of phase transition without calculating the chemical potential and the pressure of the second concurrent phase. In the second part of the review we consider phase transitions of the second kind (critical phenomena). Based on the global Gibbs approach, the Kadanov-Wilson theory of critical phenomena is analyzed. Again we use the Ornstein-Zernicke equation to formulate the local theory of critical phenomena. With regard to experimentally observable quantities this theory yields precisely the same results as the Kadanov-Wilson theory; secondly, the local approach allows predicting many previously unknown details of critical phenomena, and thirdly, the local approach paves the way towards constructing a unified theory of liquids that will describe the behavior of matter not only in the regular part of the phase diagram, but also at the critical point and in its neighborhood.