Statistical mechanics of the isothermal lane-emden equation

For classical point particles in a box Λ with potential energy H(N)=N−1(1/2) ∑i≠j=1NV(xi,xj) 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.

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