Shape-interaction dualism: unraveling complex phase behavior in triangular particle monolayers

This paper examines the effect of finite attractive and repulsive interactions on the self-assembly of triangular-shaped particles on a triangular lattice. The ground state analysis of the lattice model has revealed an infinite sequence of ordered structures, a phenomenon referred to as the 'devil's staircase' of phase transitions. The model has been studied at finite temperatures using both the transfer-matrix and tensor renormalization group methods. The concurrent use of these two methods lends credibility to the obtained results. It has been demonstrated that the initial ordered structures of the 'devil's staircase' persist at non-zero temperatures. Further increase of the attraction between particles or a decrease of the temperature induces the appearance of subsequent ordered structures of the 'devil's staircase'. The corresponding phase diagram of the model has been calculated. The phase behavior of our model agrees qualitatively with the phase behavior of trimesic acid adsorption layer on single crystal surfaces.