Fluctuations and Physical Properties of the Two-Dimensional Crystal Lattice

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 $S(\overrightarrow{\mathrm{k}},\omega )$ about the peaks is analyzed. The lattice is shown to produce a Mössbauer peak with a non-Lorentzian line shape but with a Mössbauer 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.