  Coordination-related, two-dimensional (2D) structural phase transitions are a
fascinating and novel facet of two-dimensional materials with structural
degeneracies. Nevertheless, a unified theoretical account of these transitions
remains absent, and the following points are established through {\em
ab-initio} molecular dynamics and 2D discrete clock models here: Group-IV
monochalcogenide (GeSe, SnSe, SnTe, ...) monolayers have four degenerate
structural ground states, and a 2D phase transition from a three-fold
coordinated onto a five-fold coordinated structure takes place at finite
temperature. On unstrained samples, the 2D phase transition requires lattice
parameters to freely evolve. A fundamental energy scale permits understanding
this transition. The transition temperature $T_c$ and the orientation of the
in-plane intrinsic electric dipole can be controlled by moderate uniaxial
tensile strain, and a modified discrete clock model describes the transition on
strained samples. These results establish a general underlying theoretical
background to understand structural phase transitions in 2D materials and their
effects on material properties.
