Abstract
For classical point particles in a box Λ with potential energy H(N)=N −1(1/2) ∑ Ni≠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.
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Messer, J., Spohn, H. Statistical mechanics of the isothermal lane-emden equation. J Stat Phys 29, 561–578 (1982). https://doi.org/10.1007/BF01342187
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DOI: https://doi.org/10.1007/BF01342187