EQUILIBRIUM STATISTICAL-MECHANICS OF ONE-DIMENSIONAL HAMILTONIAN-SYSTEMS WITH LONG-RANGE FORCE

The system of N identical classical particles on the circle of length L interacting via a pair potential is investigated in the mean field l imit (N-->infinity, L fixed). Its physical properties are determined b y the Fourier components of the interaction (mean) field. The partitio n function, the joint distribution of the interaction fields, the loca l field, and the correlation functions are computed. If the interactio n is semidefinite non-negative, field components become independent fo r N-->infinity and satisfy central limit theorems. If the interaction has negative Fourier components, a phase transition occurs.