Why the two-dimensional crystals were considered unstable at a certain temperature according to the Landau and Peierls Thermodynamic law? And how the perception changed after the discovery of graphene as the first two-dimensional material
As far as I know, the important law here was Hohenberg's generalization of the Mermin-Wagner-theorem:
Article Existence of Long-Range Order in One and Two Dimensions
[Don't ask me details, it's been years since I read that one.] The validity of this statement has not "fallen" so far since the graphene that has been made is always supported and terminated. A fictional, idealized infinite graphene would by this logic still be forbidden.
Edit: I just found other discussions right on this topic:
https://www.researchgate.net/post/Why_does_graphene_refuse_Mermin_weigner_theorem
https://www.researchgate.net/post/Why_there_is_no_long_range_order_in_2D_crystal
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