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Ridged, orthorhombic two-dimensional atomic crystals with a bulk {\em Pnma}structure such as black phosphorus and monochalcogenide monolayers are anexciting and novel material platform for a host of applications. Key to theircrystallinity, monolayers of these materials have a four-fold degeneratestructural ground state, and a single energy scale $E_C$ (representing theelastic energy required to switch the longer lattice vector along the $x-$ or$y-$direction) determines how disordered these monolayers are at finitetemperature. Disorder arises when nearest neighboring atoms become gentlyreassigned as the system is thermally excited beyond a critical temperature$T_c$ that is proportional to $E_C/k_B$. $E_C$ is tunable by chemicalcomposition and it leads to a classification of these materials into twocategories: (i) Those for which $E_C\ge k_BT_m$, and (ii) those having$k_BT_m>E_C\ge 0$, where $T_m$ is a given material's melting temperature. Blackphosphorus and SiS monolayers belong to category (i): these materials do notdisplay an intermediate order-disorder transition and melt directly. All othermonochalcogenide monolayers with $E_C>0$ belonging to class (ii) will undergo atwo-dimensional transition prior to melting. $E_C/k_B$ is slightly larger thanroom temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSemonolayers, so that these materials transition near room temperature. The onsetof this generic atomistic phenomena is captured by a planar Potts model up tothe order-disorder transition. The order-disorder phase transition in twodimensions described here is at the origin of the {\em Cmcm} phase beingdiscussed within the context of bulk layered SnSe.

Two-dimensional disorder in black phosphorus and monochalcogenide monolayers