Abstract
In the theory of critical phenomena of lattice models, two dimensions holds special fascination for several reasons. In this low dimensionality, fluctuations are stonger, leading to more pronounced divergences near the transition and to grosser violations of mean field predictions. In contrast to three dimensions, there are several exactly-solved models, which provide invaluable benchmarks for understanding critical properties. One of the few places one can hope to find realizations of such models is at surfaces of materials, either by adsorbed atoms or by reconstruction [11.1] of the top layer(s). Regarding reconstruction, 2D does not mean planar: In many reconstructions, several layers near the surface are involved. All that is required for the transitions to be 2D is that displacements eventually decay exponentially as one goes deep into the bulk and that there be no new periodicity exhibited by the ordered state perpendicular to the surface, just parallel to it. On the other hand, we will not consider “ordinary” surface transitions, i.e., 2D critical behavior at the surface generated by a bulk, 3D transition [11.2].
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Einstein, T.L. (1988). Critical Phenomena of Chemisorbed Atoms and Reconstruction — Revisited. In: Vanselow, R., Howe, R. (eds) Chemistry and Physics of Solid Surfaces VII. Springer Series in Surface Sciences , vol 10. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-73902-6_11
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