The influence of random pinning on the melting scenario of two-dimensional soft-disk systems

Abstract

We present the results of a computer simulation study of the melting scenario of two-dimensional soft-disk systems with potential U (r) = ε(σ/r) n , n = 12 and n = 1024, both in the presence of random pinning and without it. The melting parameters have been determined from analysis of the behavior of equations of state, correlation functions of the orientational and translational order parameters, Young modulus and renormalization group equations. The transition points obtained from these criteria are in good agreement. We have shown that the systems melted in two stages -first-order hexatic phase to liquid transition and the continuous Berezinskii-Kosterlitz-Thouless type crystal-hexatic phase transition. Random pinning widened the hexatic phase, but left the melting scenario unchanged.

The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard-Jones systems

“…At high temperatures, the effect of attraction should vanish, and only the repulsive branch of potential (1) should play a more significant role. Indeed, analyzing the melting scenarios of triangular crystals at high temperatures (and high densities), we observed that LJ12m systems demonstrated the same melting scenarios as soft disks repulsive potential 1/r 12 (the third melting scenario 14,42,45 ).…”

“…The obtained results agree well with the melting scenario for repulsive disks 1/r 12 (reported in Refs. 14,42,45 ), but do not exhibit two continuous BKT transitions in the LJ system at high temperatures 12,89 . The obtained results agree well with the melting scenario for repulsive disks 1/r 12 (reported in Refs.…”

“…The obtained results agree well with the melting scenario for repulsive disks 1/r 12 (reported in Refs. 14,42,45 ), but do not exhibit two continuous BKT transitions in the LJ system at high temperatures 12,89 . All triangular crystals, we studied, were found to melt at high temperatures via the third scenario, irrespective to the attraction index m. The melting lines in this region of the phase diagram are shifted to low densities with an increase in m and behave similarly to a system of soft disks 1/r 12 , as shown in Fig.…”

“…Thus, at low temperatures where the role of attraction is dominant all systems melt via first-order transition due to suppression of the hexatic phase. At high temperatures LJ disks melt in accordance with the third scenario, the same as soft disks 14,44,45 , whereas hexagons and squares do according to the BKTHNY theory with participation of the hexatic and tetratic phases, respectively. The melting scenario of pentagons does not change with an increase in temperature and is a first-order transition.…”

Melting scenarios of two-dimensional Hertzian spheres with a single triangular lattice

“…In computer simulations [51][52][53][54][55] and in experiments [56] it was shown that the system could melt through a continuous BKT type solid-hexatic transition, but the hexatic-liquid transition is of the first order. In paper [54] (see also [57,58]) a detailed study of a soft disk system with potential U (r) = (σ/r) n was presented. It was shown that the system melted in accordance with the BKTHNY scenario for n ≤ 6, while for n > 6 a two-stage melting transition took place with a continuous solid-hexatic and first-order hexatic-liquid transition.…”