Microphase separation as the cause of structural complexity in 2D liquids

Under certain thermodynamic conditions, a two-dimensional liquid becomes a statistically stable mosaic of small differently-ordered clusters. We apply to this mosaic a special coarsening procedure that accounts for short-time average and topologic features of a particle near environments. We then show that the coarsened mosaic consists of two different components separated at the length-scale of few inter-particle distances. Using bond order parameters and bond lengths as instant local characteristics, we show that these components have internal properties of spatially heterogeneous crystalline or amorphous phases, so the coarsened mosaic can be seen as a microphase-separated state. We discuss general conditions favouring stability of the mosaic state, and suggest some systems for searching for this special state of matter.