Inherent noise present in molecular dynamics simulations and what can be learnt from it for 2D Lennard–Jones system
https://doi.org/10.17586/2220-8054-2025-16-4-407-418
Abstract
We have investigated the influence of finite number of particles used in molecular dynamics simulations on the fluctuations of thermodynamic properties. As a case study, the two-dimensional Lennard–Jones system was used. The 2D Lennard–Jones is an archetypal system and a subject of long debate about whether it has continuous (infinite-order) or discontinuous (the first-order) melting transition. We have found, that anomalies on the equation of state (the van-der-Waals or Myer–Wood loops), previously considered a hallmark of the first order phase transition, are at best at the level of noise, since their magnitude is the same as the amplitude of pressure fluctuations. So, they could be regarded as a statistically unsignificant effect. Also, we estimated inherent statistical noise present in computer simulations, and came to the conclusion, that it is larger than predicted by statistical physics, and the difference between them (called algorithmic fluctuations) may be due to the computer-related issues.
About the Authors
M. V. Kondrin
Institute for High Pressure Physics RAS
Russian Federation
Russian Federation
Mikhail V. Kondrin
108840 Troitsk, Moscow, Russia
Yu. B. Lebed
Institute for Nuclear Research RAS
Russian Federation
Russian Federation
Yulia B. Lebed
117312 Moscow, Russia
References
1. Hickman J., Mishin Y. Temperature fluctuations in canonical systems: Insights from molecular dynamics simulations. Phys. Rev. B, 2016, 94, 184311.
2. Landau L., Pitaevskii L., Lifshitz E. Statistical Physics. Course of theoretical physics. Pergamon Press, Oxford, 1980.
3. Bystryi R.G., Lavrinenko Y.S., Lankin A.V., Morozov I.V., Norman G.E., Saitov I.M. Pressure fluctuations in nonideal nondegenerate plasma. High Temperature, 2014, 52, P. 475–482.
4. Lennard–Jones potential. URL: https://en.wikipedia.org/wiki/Lennard–Jones potential.
5. Ryzhov V.N., Gaiduk E.A., Tareeva E.E., Fomin Y.D., Tsiok E N. Melting scenarios of two-dimensional systems: Possibilities of computer simulation. J. of Experimental and Theoretical Physics, 2023, 137, P. 125–150.
6. Barker J., Henderson D., Abraham F. Phase diagram of the two-dimensional Lennard–Jones system; evidence for first-order transitions. Physica A: Statistical Mechanics and its Applications, 1981, 106 (1), P. 226–238.
7. Frenkel D., McTague J.P. Evidence for an orientationally ordered two-dimensional fluid phase from molecular-dynamics calculations. Phys. Rev. Lett., 1979, 42, P. 1632–1635.
8. Toxvaerd S. Computer simulation of melting in a two-dimensional Lennard–Jones system. Phys. Rev. A, 1981, 24, P. 2735–2742.
9. Tobochnik J., Chester G.V. Monte Carlo study of melting in two dimensions. Phys. Rev. B, 1982, 25, P. 6778–6798.
10. Koch S.W., Abraham F.F. Freezing transition of xenon on graphite: A computer-simulation study. Phys. Rev. B, 1983, 27, P. 2964–2979.
11. Bakker A.F., Bruin C., Hilhorst H.J. Orientational order at the two-dimensional melting transition. Phys. Rev. Lett., 1984, 52, P. 449–452.
12. Udink C., van der Elsken J. Determination of the algebraic exponents near the melting transition of a two-dimensional Lennard–Jones system. Phys. Rev. B, 1987, 35, P. 279–283.
13. Chen K., Kaplan T., Mostoller M. Melting in two-dimensional Lennard–Jones systems: Observation of a metastable hexatic phase. Phys. Rev. Lett., 1995, 74, P. 4019–4022.
14. Somer F.L., Canright G.S., Kaplan T., Chen K., Mostoller M. Inherent structures and two-stage melting in two dimensions. Phys. Rev. Lett., 1997, 79, P. 3431–3434.
15. Somer F.L., Canright G.S., Kaplan T. Defect-unbinding transitions and inherent structures in two dimensions. Phys. Rev. E, 1998, 58, P. 5748–5756.
16. Wierschem K., Manousakis E. Simulation of two-dimensional melting of Lennard–Jones solid. Physics Procedia, 2010, 3 (3), P. 1515–1519.
17. Patashinski A.Z., Orlik R., Mitus A.C., Grzybowski B.A., Ratner M.A. Melting in 2d Lennard–Jones systems: What type of phase transition? The J. of Physical Chemistry C, 2010, 114 (48), P. 20749–20755.
18. Wierschem K., Manousakis E. Simulation of melting of two-dimensional Lennard–Jones solids. Phys. Rev. B, 2011, 83, 214108.
19. Hajibabaei A., Kim K.S. First-order and continuous melting transitions in two-dimensional Lennard–Jones systems and repulsive disks. Phys. Rev. E, 2019, 99, 022145.
20. Li Y.-W., Ciamarra M.P. Attraction tames two-dimensional melting: From continuous to discontinuous transitions. Phys. Rev. Lett., 2020, 124, 218002.
21. Tsiok E.N., Fomin Y.D., Gaiduk E.A., Tareyeva E.E., Ryzhov V.N., Libet P.A., Dmitryuk N.A., Kryuchkov N.P., Yurchenko S.O. The role of attraction in the phase diagrams and melting scenarios of generalized 2D Lennard–Jones systems. The J. of Chemical Physics, 2022, 156 (11), 114703.
22. Plimpton S. Fast parallel algorithms for short-range molecular dynamics. J. of Computational Physics, 1995, 117 (1), P. 1–19.
23. Plimpton S., Kohlmeyer A., Thompson A., Moore S., Berger R. LAMMPS Stable release 29 September 2021.
24. Svaneborg Lab Computational soft-matter group: LAMMPS Demos. URL: http://www.zqex.dk/index.php/method/lammps-demo.
25. R Core Team. R: A language and environment for statistical computing, 2012.
26. Homes S., Mausbach P., Thol M., Nitzke I., Vrabec J. Thermodynamic properties of low-dimensional (d < 3) Lennard–Jones fluids. J. of Molecular Liquids, 2025, 429, 127529.
27. Berezinskii V.L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group i. classical systems. JETP, 1971, 32, 493.
28. Kondrin M., Lebed Y., Fomin Y., Brazhkin V. On the thermodynamic fluctuations in computer simulations. Physics-Uspekhi, 2025, accepted.
29. Tsiok E.N., Gaiduk E.A., Fomin Y.D., Ryzhov V.N. Melting scenarios of two-dimensional hertzian spheres with a single triangular lattice. Soft Matter, 2020, 16, P. 3962–3972.
30. Frenkel D., Smit B. Understanding molecular simulation (From Algorithms to Applications), 2nd Edition. Academic Press, 2002.
31. Kubo R. The fluctuation-dissipation theorem. Reports on Progress in Physics, 1966, 29 (1), 255.
32. Kondrin M.V., Brazhkin V.V., Lebed Y.B. Fluctuation-dissipation theorem and the dielectric response in supercooled liquids. The J. of Chemical Physics, 2015, 142 (10), 104505.
33. Danilov I., Pronin A., Gromnitskaya E., Kondrin M., Lyapin A., Brazhkin V. Structural and Dielectric Relaxations in Vitreous and Liquid State of Monohydroxy Alcohol at High Pressure. The J. of Physical Chemistry B, 2017, 121 (34), P. 8203–8210.
34. Gromnitskaya E., Stal’gorova O., Yagafarov O., Brazhkin V., Lyapin A., Popova S. Ultrasonic study of the phase diagram of methanol. JETP Letters, 2004, 80 (9), P. 597–601.
35. Lebowitz J.L., Percus J.K., Verlet L. Ensemble dependence of fluctuations with application to machine computations. Phys. Rev., 1967, 153, P. 250–254.
36. Ray J.R., Graben H. Direct calculation of fluctuation formulae in the microcanonical ensemble. Molecular Physics, 1981, 43 (6), P. 1293–1297.
Review
For citations:
Kondrin M.V., Lebed Yu.B. Inherent noise present in molecular dynamics simulations and what can be learnt from it for 2D Lennard–Jones system. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(4):407-418. https://doi.org/10.17586/2220-8054-2025-16-4-407-418
Views:
128
Email this article 