Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Letter
  • Access by Xinjiang University

Athermal tricriticality

Mauro Sellitto*

  • *Contact author: mauro.sellitto@unicampania.it

Phys. Rev. E 111, L042101 – Published 7 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.L042101

Abstract

I construct a two dimensional monodisperse lattice gas model with selective geometric constraints featuring a fluid-solid continuous phase transition on the square lattice and a dimerized ground state with fourfold degeneracy. Finite-size scaling analysis confirms that the lattice gas belongs to the universality class of two-dimensional four-state Potts model, and since its thermodynamics is governed by entropy alone, this provides possibly the simplest statistical mechanical realization of an athermal tricritical point.

Physics Subject Headings (PhySH)

Article Text

References (45)

  1. J. N. Israelachvili, Intermolecular and Surface Forces (Academic, London, 1991).
  2. P. Nelson, Biological Physics: Energy, Information, Life (Freeman, New York, 2004).
  3. D. Frenkel, Nat. Mater. 14, 9 (2015).
  4. F. A. Escobedo, Soft Matter 10, 8388 (2014).
  5. For an interesting account of the early history of tricritical points and attempts to locate them experimentally, see: C. M. Knobler and R. M. Scott, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz, Vol. 9 (Academic, London, 1984).
  6. For a review of the theory of tricritical points, see: I. D. Lawrie and S. Serbach, in Phase Transitions and Critical Phenomena, edited by C. Domb and J. Lebowitz, Vol. 9 (Academic, London, 1984).
  7. M. Blume, V. J. Emery, and R. B. Griffiths, Phys. Rev. A 4, 1071 (1971).
  8. P.-G. de Gennes, J. Physique Lett. 36, 55 (1975); P.-G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaka and London, 1979).
  9. H. Kleinert, Lett. Nuovo Cimento 35, 405 (1982).
  10. S. Chandrasekhar, Liquid Crystals (Cambridge University Press, New York, 1992).
  11. P. de Forcrand and O. Philipsen, Phys. Rev. Lett. 105, 152001 (2010).
  12. F. J. Wegner and E. K. Riedel, Phys. Rev. B 7, 248 (1973).
  13. M. denNijs, Phys. Rev. B 27, 1674 (1983).
  14. B. Nienhuis, J. Stat. Phys. 34, 731 (1984).
  15. A. A. Belavin, A. M. Polyakov, and A. B. Zamolodchikov, J. Stat. Phys. 34, 763 (1984).
  16. D. Friedan, Z. Qiu, and S. Shenker, Phys. Rev. Lett. 52, 1575 (1984).
  17. V. S. Dotsenko and V. A. Fateev, Nucl. Phys. B 240, 312 (1984).
  18. M. W. Springgate and D. Poland, Phys. Rev. A 20, 1267 (1979).
  19. D. A. Huse, Phys. Rev. Lett. 49, 1121 (1982).
  20. R. J. Baxter and P. A. Pearce, J. Phys. A: Math. Gen. 16, 2239 (1983).
  21. T. J. Oliveira and J. F. Stilck, Phys. Rev. E 92, 032101 (2015).
  22. G. Biroli and M. Mézard, Phys. Rev. Lett. 88, 025501 (2001).
  23. R. K. Darst, D. R. Reichman, and G. Biroli, J. Chem. Phys. 132, 044510 (2010).
  24. R. J. Baxter, J. Phys. C: Solid State Phys. 6, L445 (1973).
  25. H. C. M. Fernandes, Y. Levin, and J. J. Arenzon, J. Chem. Phys. 126, 114508 (2007).
  26. X. Feng, H. W. J. Blöte, and B. Nienhuis, Phys. Rev. E 83, 061153 (2011).
  27. K. Ramola and D. Dhar, Phys. Rev. E 86, 031135 (2012).
  28. T. Nath and R. Rajesh, Phys. Rev. E 90, 012120 (2014).
  29. K. Ramola, K. Damle, and D. Dhar, Phys. Rev. Lett. 114, 190601 (2015).
  30. T. Nath and R. Rajesh, J. Stat. Mech. (2016) 073203.
  31. F. C. Thewes and H. C. M. Fernandes, Phys. Rev. E 101, 062138 (2020).
  32. G. Kamieniarz and H. W. J. Blöte, J. Phys. A: Math. Gen. 26, 6679 (1993).
  33. W. Guo and H. W. J. Blöte, Phys. Rev. E 66, 046140 (2002).
  34. M. Sellitto, J. Chem. Phys. 156, 124105 (2022).
  35. M. Sellitto, Phys. Rev. E 105, 054101 (2022).
  36. M. Sellitto, J. Chem. Phys. 161, 224102 (2024).
  37. M. Sellitto, J. Stat. Phys. (to be published).
  38. K. Binder, Z. Phys. B 43, 119 (1981).
  39. M. Newman and G. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, New York, 1999).
  40. R. Dickman, J. Chem. Phys. 136, 174105 (2012).
  41. R. J. Baxter, Exactly Solved Models Statistical in Mechanics (Academic Press, London, 1982).
  42. M. Nauenberg and D. J. Scalapino, Phys. Rev. Lett. 44, 837 (1980).
  43. J. L. Cardy, M. Nauenberg, and D. J. Scalapino, Phys. Rev. B 22, 2560 (1980).
  44. J. Salas and A. D. Sokal, J. Stat. Phys. 88, 567 (1997).
  45. M. Sellitto, Three-state Potts universality in a lattice gas with selective geometric constraint (unpublished).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation