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The properties of finite, but large, two-dimensional crystal lattices are discussed in the light of the lack of long-range order. We confirm, with qualifications, the important basic result that the susceptibility diverges below a critical temperature. The details of our previous paper on Bragg peaks in scattering from the two-dimensional lattice are presented and the behavior of the dynamic structure factor S (k, ) about the peaks is analyzed. The lattice is shown to produce a M\"ossbauer peak with a non-Lorentzian line shape but with a M\"ossbauer strength of the same order of magnitude as that of the three-dimensional lattice. Finally, it is argued that finite phonon lifetimes would affect our results quantitatively but not qualitatively.
Imry et al. (Tue,) studied this question.