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Two-dimensional Rydberg atoms are modeled at low temperatures by means of theclassical Monte Carlo method. The Coulomb repulsion of charged ions competingwith the repulsive van der Waals long-range tail is modeled by a number ofinteraction potentials. We find that under specific conditions the usualtriangular crystal becomes unstable with respect to more exotic lattices suchas Kagom\'e, flower, molecular crystal and rectangular chain packings.Ground-state configurations are obtained by means of the annealing procedureand their stability is additionally studied by the normal modes analysis. Whilecommonly the square lattice is mechanically unstable due to softening of theshear modulus, we were able to find a specific set of parameters for which thesquare lattice can be made stable.

Spontaneous formation of Kagom\'e lattice in two-dimensional Rydberg atoms