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Statistical Mechanics of Freely Fluctuating Two-Dimensional Elastic Crystals

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Abstract

In this paper, some facts related Joel L. Lebowitz are mentioned. In addition, some of the known theory concerning the statistical physics of freely fluctuating two-dimensional crystals subject to a non-linear elastic hamiltonian is described. Particular topics that are discussed include the existence of two-dimensional crystals in relation to the Hohenberg–Mermin–Wagner theorem, the crumpling transition for freely suspended crystalline membranes and the renormalization of elastic moduli. Although much of what is known has been uncovered since the mid-80s, the topic has become of interest once again due to the discovery of graphene and other two-dimensional crystals. The field is vast so it is the aim of this note to describe some of its fundamental properties.

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Acknowledgements

The authors thank Andrej Košmrlj for many useful discussions and reading the manuscript in preparation. We also would like to thank Siddhartha Sarkar for reading the manuscript in preparation. The first author would like to acknowledge the support of the NSF DMR-1752100 Grant.

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  1. Princeton University, Princeton, NJ, USA

    M. E. H. Bahri & Y. Sinai

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  1. M. E. H. Bahri
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  2. Y. Sinai
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Correspondence to M. E. H. Bahri.

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Communicated by Ivan Corwin.

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Bahri, M.E.H., Sinai, Y. Statistical Mechanics of Freely Fluctuating Two-Dimensional Elastic Crystals. J Stat Phys 180, 739–748 (2020). https://doi.org/10.1007/s10955-020-02512-4

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