# A Proof of Crystallization in Two Dimensions

@article{Theil2006APO,
title={A Proof of Crystallization in Two Dimensions},
author={Florian Theil},
journal={Communications in Mathematical Physics},
year={2006},
volume={262},
pages={209-236}
}
• F. Theil
• Published 1 February 2006
• Computer Science
• Communications in Mathematical Physics
Many materials have a crystalline phase at low temperatures. The simplest example where this fundamental phenomenon can be studied are pair interaction energies of the type where y(x) ∈ℝ2 is the position of particle x and V(r) ∈ ℝ is the pair-interaction energy of two particles which are placed at distance r. Due to the Mermin-Wagner theorem it can't be expected that at finite temperature this system exhibits long-range ordering. We focus on the zero temperature case and show rigorously that…
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