Statistical mechanics of the isothermal lane-emden equation

Abstract

For classical point particles in a box Λ with potential energy H^(N)=N ⁻¹(1/2) ∑ ^N_i≠j=1 V(x _i,x _j) we investigate the canonical ensemble for largeN. We prove that asN→∞ the correlation functions are determined by the global minima of a certain free energy functional. Locally the distribution of particles is given by a superposition of Poisson fields. We study the particular case Λ=[−πL, πL] andV(x, y)=}-β cos(x−y),L}>0, β}>0.