Statistical mechanics of freely fluctuating two-dimensional elastic crystals (Q2194184)

The paper is dedicated to Joel Lebowitz and recalls his personal and scientific encounters with Y. Sinai, common scientific interests and joint publications. Although no original new results are presented, some known theory concerning the statistical physics of freely fluctuating two-dimensional crystals subject to a non-linear elastic Hamiltonian is described. In particular, a discovery of graphene, a two-dimensional crystal, gave impetus to theoretical attempts towards reconciling their existence with the Mermin-Wagner theorem and the crumpling phase transition issue for freely suspended crystalline membranes. The renormalizaton of elastic moduli of graphene has been addressed as well. ``Although much of what is known has been uncovered since the mid-80s, the topic has become of interest once again due to the discovery of graphene and other two-dimensional crystals. The field is vast so it is the aim of this note to describe some of its fundamental properties.''