Abstract
We consider a classical system of \(N\) particles confined in a box \(\Lambda \subset \mathbb {R}^d\) interacting via a finite range pair potential. Given the validity of the cluster expansion in the canonical ensemble we compute the error between the finite and the infinite volume free energy and estimate it to be bounded by the area of the surface of the box’s boundary over its volume. We also compute the truncated two-point correlation function and find that the contribution from the ideal gas case is of the order \(1/|\Lambda |\) plus an exponentially small error with the distance.
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Acknowledgments
It is a great pleasure to thank Errico Presutti for suggesting us the problem and for his continuous advising. We also acknowledge discussions with Marzio Cassandro, Sabine Jansen and Thierry Bodineau who gave us intuition about the estimate of Theorem 2.5. Moreover, we are indebted to one of the referees for the careful revision of the manuscript and the detailed comments for the improvement of the presentation. The research of both authors was partially supported by the FP7-REGPOT-2009-1 project “Archimedes Center for Modeling, Analysis and Computation” (under grant agreement no 245749). E. P. is further supported by ERC Advanced Grant 267356 VARIS of Frank den Hollander.
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Pulvirenti, E., Tsagkarogiannis, D. Finite Volume Corrections and Decay of Correlations in the Canonical Ensemble. J Stat Phys 159, 1017–1039 (2015). https://doi.org/10.1007/s10955-015-1207-z
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DOI: https://doi.org/10.1007/s10955-015-1207-z