On a global minimum of potential energy in molecular statics: An example of a 2D Lennard-Jones crystal

The effect of convergence with a prescribed accuracy to a local minimum on structural properties of the crystal, such as stress–strain curves, dislocations initiation, distributions of interatomic forces, is investigated on 2D LJ crystal with one deficiency for both tensile and cyclic deformations. It is shown that the associated structural properties of the crystal strongly depend on the specified level of numerical accuracy. It also found that during the cyclic deformation a hysteretic loop is formed. The latter is called a numerical hysteresis since theoretically it must vanish at the global minimum. The trend of the area of the hysteretic loop to zero with increasing accuracy is investigated numerically.