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 $U\left(r\right)=\epsilon (\sigma /r{)}^n$, 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 behaviour of equations of state, correlation functions of the orientational and translational order parameters, Young modulus and renormalisation 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.

GRAPHICAL ABSTRACT

KEYWORDS:

• Two-dimensional melting
• soft disks
• Berezinskii–Kosterlitz–Thouless transition
• correlation functions
• renormalisation group equations

PACS numbers:

• 61.20.Gy
• 61.20.Ne
• 64.60.Kw

Acknowledgments

The authors are grateful to E.E. Tareyeva, S.M. Stishov and V.V. Brazhkin for valuable discussions. This work was carried out using computing resources of the federal collective usage centre “Complex for simulation and data processing for mega-science facilities” at NRC “Kurchatov Institute”, http://ckp.nrcki.ru, and supercomputers at Joint Supercomputer Center of the Russian Academy of Sciences (JSCC RAS). The work was supported by the Russian Science Foundation (Grant 19-12-00092). 

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Russian Foundation for Basic Research (Grants No 17-02-00320 (VNR) and 18-02-00981 (YDF)).