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Phase transition from nematic to HDD phase in hard rods

Systems of hard rods are studied for a long time as it shows rich behavior in a statistical physics perspective. The problem got a first breakthrough when Lars Onsager in 1940s provided an exact calculation where he showed there is a phase transition from disordered to a nematic phase. This is intuitively also understandable if one thinks about a box of needles with fix number of density of needles. If you increase the density you will see that needles prefer to orient in one direction rather than be in any random orientation. This transition is settled. After about 60 years Ghosh A. and Dhar D. studied this problem numerically using efficient Monte-Carlo algorithm and showed evidence that if one further increases the density this ordered nematic state becomes unstable and we reach to a high density disordered (HDD) phase. On lattice if the length of a needle is k then this transition was interestingly seen only for k>6. The understanding of HDD phase is still an open (and rather a hard) problem. In 2022, Shah et al. argued that the instability of the nematic phase and provided an understanding of why the second transition (observed only for k > 6) is entropy-driven. Similar models have also been studied on lattices such as the kagome lattice, which is of interest here.

References

  1. L. Onsager, The effects of shape on the interaction of colloidal particles, Annals of the New York Academy of Sciences 51, 627–659 (1949).
  2. A. Ghosh and D. Dhar, On the orientational ordering of long rods on a lattice, EPL 78, 20003 (2007).
  3. A. Shah, D. Dhar and R. Rajesh et al., The phase transition from nematic to high-density disordered phase in a system of hard rods on a lattice Phys. Rev. E 105, 034103 (2022).
  4. D. Dhar, R. Rajesh, and J. F. Stilck, Hard rigid rods on a Bethe-like lattice, Phys. Rev. E 84, 011140 (2011).
  5. J. Kundu, R. Rajesh, D. Dhar, and J. F. Stilck, A Monte Carlo algorithm for studying phase transition in systems of hard rigid rods, AIP Conf. Proc. 1447, 113 (2012).
  6. J. Kundu, R. Rajesh, D. Dhar, and J. F. Stilck, Nematic-disordered phase transition in systems of long rigid rods on two-dimensional lattices, Phys. Rev. E 87, 032103 (2013).
  7. J. Kundu and R. Rajesh, Reentrant disordered phase in a system of repulsive rods on a Bethe-like lattice, Phys. Rev. E 88, 012134 (2013).
  8. N. Vigneshwar, D. Dhar, and R. Rajesh, Different phases of a system of hard rods on three dimensional cubic lattice, J. Stat. Mech. 113304 (2017).
  9. D. Dhar and R. Rajesh, Entropy of fully packed hard rigid rods on d-dimensional hypercubic lattices, Phys. Rev. E 103, 042130 (2021).
  10. A. A. A. Jaleel, J. E. Thomas, D. Mandal, Sumedha, and R. Rajesh, Rejection free cluster Wang-Landau algorithm for hard core lattice gases, arXiv:2108.01402 (2021).
  11. A. A. A. Jaleel, D. Mandal, and R. Rajesh, Hard core lattice gas with third next-nearest neighbor exclusion on triangular lattice, arXiv:2108.03547 (2021).
  12. J. Kundu and R. Rajesh, Phase transitions in a system of hard rectangles on the square lattice, Phys. Rev. E 89, 052124 (2014).
  13. J. Kundu and R. Rajesh, Phase transitions in systems of hard rectangles with non-integer aspect ratio, Eur. Phys. J. B 88, 133 (2015).
  14. J. Kundu and R. Rajesh, Asymptotic behavior of the isotropic-nematic and nematic-columnar phase boundaries, Phys. Rev. E 91, 012105 (2015).

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