- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Irreversible swap algorithms for soft sphere glasses

Yoshihiko Nishikawa1,2, Federico Ghimenti3,4, Ludovic Berthier5, and Frédéric van Wijland3,6

PDF

Phys. Rev. E 111, 045416 – Published 17 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.045416

Abstract

We extend to soft repulsive interaction potentials a recently proposed irreversible swap algorithm originally designed for polydisperse hard spheres. The original algorithm performs rejection-free, irreversible, collective swap moves. We show that event-driven cluster updates of particle diameters can also be performed in continuous potentials by introducing a factorized Metropolis probability. However, the Metropolis factorization needed to deal with continuous potentials decreases the efficiency of the algorithm and mitigates the benefits of breaking detailed balance. This leads us to propose another irreversible swap algorithm using the standard Metropolis probability that accelerates the relaxation of soft sphere glasses at low temperatures compared to the original swap algorithm. We apply these efficient swap algorithms to produce very stable inherent structures with vibrational density of states lacking the quasilocalized excitations observed in conventional glasses.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (83)

  1. L. Berthier and G. Biroli, Theoretical perspective on the glass transition and amorphous materials, Rev. Mod. Phys. 83, 587 (2011).
  2. L. Berthier and D. R. Reichman, Modern computational studies of the glass transition, Nat. Rev. Phys. 5, 102 (2023).
  3. L. Berthier and W. Kob, The Monte Carlo dynamics of a binary Lennard-Jones glass-forming mixture, J. Phys.: Condens. Matter 19, 205130 (2007).
  4. D. Levin and Y. Peres, Markov Chains and Mixing Times (American Mathematical Society, Providence, Rhode Island, 2017).
  5. M. E. Newman and G. T. Barkema, Monte Carlo Methods in Statistical Physics (Clarendon Press, New York, 1999).
  6. W. Krauth, Statistical Mechanics: Algorithms and Computations (Oxford University Press, Oxford, 2006), Vol. 13.
  7. R. H. Swendsen and J.-S. Wang, Nonuniversal critical dynamics in Monte Carlo simulations, Phys. Rev. Lett. 58, 86 (1987).
  8. U. Wolff, Collective Monte Carlo updating for spin systems, Phys. Rev. Lett. 62, 361 (1989).
  9. B. A. Berg and T. Neuhaus, Multicanonical ensemble: A new approach to simulate first-order phase transitions, Phys. Rev. Lett. 68, 9 (1992).
  10. E. Marinari and G. Parisi, Simulated tempering: A new Monte Carlo scheme, Europhys. Lett. 19, 451 (1992).
  11. C. Dress and W. Krauth, Cluster algorithm for hard spheres and related systems, J. Phys. A: Math. Gen. 28, L597 (1995).
  12. K. Hukushima and K. Nemoto, Exchange Monte Carlo method and application to spin glass simulations, J. Phys. Soc. Jpn. 65, 1604 (1996).
  13. L. Santen and W. Krauth, Absence of thermodynamic phase transition in a model glass former, Nature (London) 405, 550 (2000).
  14. F. Wang and D. P. Landau, Efficient, multiple-range random walk algorithm to calculate the density of states, Phys. Rev. Lett. 86, 2050 (2001).
  15. Q. Yan, T. S. Jain, and J. J. de Pablo, Density-of-states Monte Carlo simulation of a binary glass, Phys. Rev. Lett. 92, 235701 (2004).
  16. L. Berthier, Overlap fluctuations in glass-forming liquids, Phys. Rev. E 88, 022313 (2013).
  17. R. L. Jack and J. P. Garrahan, Phase transition for quenched coupled replicas in a plaquette spin model of glasses, Phys. Rev. Lett. 116, 055702 (2016).
  18. L. Berthier, P. Charbonneau, and S. Yaida, Efficient measurement of point-to-set correlations and overlap fluctuations in glass-forming liquids, J. Chem. Phys. 144, 024501 (2016).
  19. Y. Nishikawa and K. Hukushima, Lattice glass model in three spatial dimensions, Phys. Rev. Lett. 125, 065501 (2020).
  20. B. Guiselin, L. Berthier, and G. Tarjus, Random-field Ising model criticality in a glass-forming liquid, Phys. Rev. E 102, 042129 (2020).
  21. T. S. Grigera and G. Parisi, Fast Monte Carlo algorithm for supercooled soft spheres, Phys. Rev. E 63, 045102(R) (2001).
  22. L. Berthier, D. Coslovich, A. Ninarello, and M. Ozawa, Equilibrium sampling of hard spheres up to the jamming density and beyond, Phys. Rev. Lett. 116, 238002 (2016).
  23. A. Ninarello, L. Berthier, and D. Coslovich, Models and algorithms for the next generation of glass transition studies, Phys. Rev. X 7, 021039 (2017).
  24. L. Berthier, E. Flenner, C. J. Fullerton, C. Scalliet, and M. Singh, Efficient swap algorithms for molecular dynamics simulations of equilibrium supercooled liquids, J. Stat. Mech. (2019) 064004.
  25. A. D. S. Parmar, M. Ozawa, and L. Berthier, Ultrastable metallic glasses in silico, Phys. Rev. Lett. 125, 085505 (2020).
  26. B. Guiselin, C. Scalliet, and L. Berthier, Microscopic origin of excess wings in relaxation spectra of supercooled liquids, Nat. Phys. 18, 468 (2022).
  27. C. Scalliet, B. Guiselin, and L. Berthier, Thirty milliseconds in the life of a supercooled liquid, Phys. Rev. X 12, 041028 (2022).
  28. P. K. Bommineni, N. R. Varela-Rosales, M. Klement, and M. Engel, Complex crystals from size-disperse spheres, Phys. Rev. Lett. 122, 128005 (2019).
  29. P. K. Bommineni, M. Klement, and M. Engel, Spontaneous crystallization in systems of binary hard sphere colloids, Phys. Rev. Lett. 124, 218003 (2020).
  30. G. Alfaro Miranda, L. F. Cugliandolo, and M. Tarzia, SWAP algorithm for lattice spin models, Phys. Rev. E 110, L043301 (2024).
  31. Y. Nishikawa and L. Berthier, Collective relaxation dynamics in a three-dimensional lattice glass model, Phys. Rev. Lett. 132, 067101 (2024).
  32. K. Shiraishi and L. Berthier, Characterizing the slow dynamics of the swap Monte Carlo algorithm, J. Phys. Chem. B 128, 12279 (2024).
  33. C.-R. Hwang, S.-Y. Hwang-Ma, and S.-J. Sheu, Accelerating Gaussian diffusions, Ann. Appl. Probab. 3 (1993).
  34. F. Chen, L. Lovász, and I. Pak, Lifting Markov chains to speed up mixing, in Proceedings of the Thirty-first Annual ACM Symposium on Theory of Computing (ACM, New York, 1999), pp. 275–281.
  35. P. Diaconis, S. Holmes, and R. M. Neal, Analysis of a nonreversible Markov chain sampler, Ann. Appl. Probab. 10, 726 (2000).
  36. C.-R. Hwang, S.-Y. Hwang-Ma, and S.-J. Sheu, Accelerating diffusions, Ann. Appl. Probab. 15, 1433 (2005).
  37. F. Ghimenti, L. Berthier, G. Szamel, and F. van Wijland, Sampling efficiency of transverse forces in dense liquids, Phys. Rev. Lett. 131, 257101 (2023).
  38. K. S. Turitsyn, M. Chertkov, and M. Vucelja, Irreversible Monte Carlo algorithms for efficient sampling, Physica D 240, 410 (2011).
  39. M. Vucelja, Lifting—A nonreversible Markov chain Monte Carlo algorithm, Am. J. Phys. 84, 958 (2016).
  40. E. P. Bernard, W. Krauth, and D. B. Wilson, Event-chain Monte Carlo algorithms for hard-sphere systems, Phys. Rev. E 80, 056704 (2009).
  41. E. P. Bernard and W. Krauth, Two-step melting in two dimensions: First-order liquid-hexatic transition, Phys. Rev. Lett. 107, 155704 (2011).
  42. Y. Sakai and K. Hukushima, Dynamics of one-dimensional Ising model without detailed balance condition, J. Phys. Soc. Jpn. 82, 064003 (2013).
  43. M. Michel, S. C. Kapfer, and W. Krauth, Generalized event-chain Monte Carlo: Constructing rejection-free global-balance algorithms from infinitesimal steps, J. Chem. Phys. 140, 054116 (2014).
  44. M. Michel, J. Mayer, and W. Krauth, Event-chain Monte Carlo for classical continuous spin models, Europhys. Lett. 112, 20003 (2015).
  45. W. Krauth, Event-chain monte carlo: Foundations, applications, and prospects, Front. Phys. 9, 663457 (2021).
  46. T. Guyon, A. Guillin, and M. Michel, Necessary and sufficient symmetries in event-chain Monte Carlo with generalized flows and application to hard dimers, J. Chem. Phys. 160, 024117 (2024).
  47. A. Monemvassitis, A. Guillin, and M. Michel, PDMP characterisation of event-chain Monte Carlo algorithms for particle systems, J. Stat. Phys. 190, 66 (2023).
  48. F. Ghimenti, L. Berthier, and F. van Wijland, Irreversible Monte Carlo algorithms for hard disk glasses: From Event-Chain to Collective Swaps, Phys. Rev. Lett. 133, 028202 (2024).
  49. L. Berthier, F. Ghimenti, and F. van Wijland, Monte Carlo simulations of glass-forming liquids beyond Metropolis, J. Chem. Phys. 161, 114105 (2024).
  50. Y. Nishikawa, M. Michel, W. Krauth, and K. Hukushima, Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling, Phys. Rev. E 92, 063306 (2015).
  51. D. E. Knuth, The Art of Computer Programming, Vol. 3: Sorting and Searching, 2nd ed. (Addison Wesley Longman Publishing Co., Inc., Reading, MA, 1998).
  52. L. Berthier, P. Charbonneau, A. Ninarello, M. Ozawa, and S. Yaida, Zero-temperature glass transition in two dimensions, Nat. Commun. 10, 1508 (2019).
  53. E. Flenner and G. Szamel, Fundamental differences between glassy dynamics in two and three dimensions, Nat. Commun. 6, 7392 (2015).
  54. S. Sastry, P. G. Debenedetti, and F. H. Stillinger, Signatures of distinct dynamical regimes in the energy landscape of a glass-forming liquid, Nature (London) 393, 554 (1998).
  55. A. S. Keys, L. O. Hedges, J. P. Garrahan, S. C. Glotzer, and D. Chandler, Excitations are localized and relaxation is hierarchical in glass-forming liquids, Phys. Rev. X 1, 021013 (2011).
  56. E. Bitzek, P. Koskinen, F. Gähler, M. Moseler, and P. Gumbsch, Structural relaxation made simple, Phys. Rev. Lett. 97, 170201 (2006).
  57. M. Goldstein, Viscous liquids and the glass transition: A potential energy barrier picture, J. Chem. Phys. 51, 3728 (1969).
  58. F. H. Stillinger and T. A. Weber, Hidden structure in liquids, Phys. Rev. A 25, 978 (1982).
  59. F. H. Stillinger, Supercooled liquids, glass transitions, and the Kauzmann paradox, J. Chem. Phys. 88, 7818 (1988).
  60. F. H. Stillinger, A topographic view of supercooled liquids and glass formation, Science 267, 1935 (1995).
  61. J. Kurchan and L. Laloux, Phase space geometry and slow dynamics, J. Phys. A: Math. Gen. 29, 1929 (1996).
  62. S. Büchner and A. Heuer, Potential energy landscape of a model glass former: Thermodynamics, anharmonicities, and finite size effects, Phys. Rev. E 60, 6507 (1999).
  63. F. Sciortino, W. Kob, and P. Tartaglia, Inherent structure entropy of supercooled liquids, Phys. Rev. Lett. 83, 3214 (1999).
  64. F. Sciortino, Potential energy landscape description of supercooled liquids and glasses, J. Stat. Mech. (2005) P05015.
  65. A. Heuer, Exploring the potential energy landscape of glass-forming systems: From inherent structures via metabasins to macroscopic transport, J. Phys.: Condens. Matter 20, 373101 (2008).
  66. D. Khomenko, C. Scalliet, L. Berthier, D. R. Reichman, and F. Zamponi, Depletion of two-level systems in ultrastable computer-generated glasses, Phys. Rev. Lett. 124, 225901 (2020).
  67. Y. Nishikawa, M. Ozawa, A. Ikeda, P. Chaudhuri, and L. Berthier, Relaxation dynamics in the energy landscape of glass-forming liquids, Phys. Rev. X 12, 021001 (2022).
  68. E. Lerner, G. Düring, and E. Bouchbinder, Statistics and properties of low-frequency vibrational modes in structural glasses, Phys. Rev. Lett. 117, 035501 (2016).
  69. H. Mizuno, H. Shiba, and A. Ikeda, Continuum limit of the vibrational properties of amorphous solids, Proc. Natl. Acad. Sci. USA 114, E9767 (2017).
  70. G. Kapteijns, E. Bouchbinder, and E. Lerner, Universal nonphononic density of states in 2D, 3D, and 4D glasses, Phys. Rev. Lett. 121, 055501 (2018).
  71. L. Wang, A. Ninarello, P. Guan, L. Berthier, G. Szamel, and E. Flenner, Low-frequency vibrational modes of stable glasses, Nat. Commun. 10, 26 (2019).
  72. C. Brito, E. Lerner, and M. Wyart, Theory for swap acceleration near the glass and jamming transitions for continuously polydisperse particles, Phys. Rev. X 8, 031050 (2018).
  73. G. Kapteijns, W. Ji, C. Brito, M. Wyart, and E. Lerner, Fast generation of ultrastable computer glasses by minimization of an augmented potential energy, Phys. Rev. E 99, 012106 (2019).
  74. V. F. Hagh, S. R. Nagel, A. J. Liu, M. L. Manning, and E. I. Corwin, Transient learning degrees of freedom for introducing function in materials, Proc. Natl. Acad. Sci. USA 119, e2117622119 (2022).
  75. V. Bolton-Lum, R. C. Dennis, P. Morse, and E. Corwin, The ideal glass and the ideal disk packing in two dimensions, arXiv:2404.07492.
  76. B. J. Alder and T. E. Wainwright, Phase transition for a hard sphere system, J. Chem. Phys. 27, 1208 (1957).
  77. J. Liu and E. Luijten, Rejection-free geometric cluster algorithm for complex fluids, Phys. Rev. Lett. 92, 035504 (2004).
  78. E. A. J. F. Peters and G. de With, Rejection-free Monte Carlo sampling for general potentials, Phys. Rev. E 85, 026703 (2012).
  79. A. Bouchard-Côté, S. J. Vollmer, and A. Doucet, The bouncy particle sampler: A nonreversible rejection-free Markov chain Monte Carlo method, J. Am. Stat. Assoc. 113, 855 (2018).
  80. D. C. Rapaport, The Art of Molecular Dynamics Simulation (Cambridge University Press, Cambridge, 2004).
  81. L. Galliano, R. Rende, and D. Coslovich, Policy-guided Monte Carlo on general state spaces: Application to glass-forming mixtures, J. Chem. Phys. 161, 064503 (2024).
  82. G. Jung, G. Biroli, and L. Berthier, Normalizing flows as an enhanced sampling method for atomistic supercooled liquids, Mach. Learn.: Sci. Technol. 5, 035053 (2024).
  83. https://doi.org/10.5281/zenodo.15178992.

Outline

Information

Phys. Rev. E 111, 045416– Published 17 April, 2025
  • Received 27 January 2025
  • Accepted 28 March 2025
Crossmark - Check for updates button

©2025 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation