Foundations of Statistical Mechanics and Theory of Phase Transition

Details Foundations of Statistical Mechanics and Theory of Phase Transition Foundations of Statistical Mechanics and Theory of Phase Transition

1997-03-03

arxiv.org/abs/physics/9703007v1

Physics

Mathematical Physics

19 pages, Latex

Scientific paper

A new formulation of statistical mechanics is put forward according to which a random variable characterizing a macroscopic body is postulated to be infinitely divisible. It leads to a parametric representation of partition function of an arbitrary macroscopic body, a possibility to describe a macroscopic body under excitation by a gas of some elementary quasiparticles etc. A phase transition is defined as such a state of a macroscopic body that its random variable is stable in sense of L\'evy. From this definition it follows by deduction all general properties of phase transitions: existence of the renormalization semigroup, the singularity classification for thermodynamic functions, the phase transition universality and universality classes. On this basis we has also built a 2-parameter scaling theory of phase transitions, a thermodynamic function for the Ising model etc.

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