Phase diagram of a double-occupancy cell model of a fluid with Curie-Weiss interaction
DOI:
https://doi.org/10.5488/cmp.29.33603Keywords:
double-occupancy cell model, Blume-Capel model, liquid-liquid phase transition, liquid-liquid critical pointAbstract
A double-occupancy cell model of a fluid with Curie-Weiss interaction is studied. First, we show that the model is isomorphic to the Blume-Capel model on a complete graph through a simple transformation from spin to occupancy variables. We then investigate its phase behavior within the grand-canonical ensemble using a combination of analytical and numerical methods. Despite its simplicity, the model exhibits a remarkably rich thermodynamic behavior depending on the ratio between the local repulsive and global attractive interactions. We identify the regimes characterized by a single critical point, two distinct critical points, tricritical behavior, and triple-point formation. For sufficiently strong repulsion, the system possesses three fluid phases of different densities, leading to both gas-liquid and liquid-liquid coexistence. The locations of the critical, tricritical, and triple points are determined, and the corresponding phase diagrams are constructed. These results demonstrate that the competition between double-occupancy repulsion and long-range attraction is sufficient to generate a complex phase behavior in a minimal multiple-occupancy lattice-gas-like model.
References
Likos C. N., Phys. Rep., 2001, 348, No. 4, 267–439. DOI: https://doi.org/10.1016/S0370-1573(00)00141-1
Louis A. A., Bolhuis P. G., Hansen J. P., Meijer E. J., Phys. Rev. Lett., 2000, 85, 2522–2525. DOI: https://doi.org/10.1103/PhysRevLett.85.2522
Bolhuis P. G., Louis A. A., Hansen J. P., Meijer E. J., J. Chem. Phys., 2001, 114, No. 9, 4296–4311. DOI: https://doi.org/10.1063/1.1344606
Likos C. N., Schmidt M., Löwen H., Ballauff M., Pötschke D., Lindner P., Macromolecules, 2001, 34, 2914–2920. DOI: https://doi.org/10.1021/ma001346x
Mladek B. M., Kahl G., Likos C. N., Phys. Rev. Lett., 2008, 100, 028301. DOI: https://doi.org/10.1103/PhysRevLett.100.028301
Likos C. N., Löwen H., Watzlawek M., Abbas B., Jucknischke O., Allgaier J., Richter D., Phys. Rev. Lett., 1998, 80, 4450–4453. DOI: https://doi.org/10.1103/PhysRevLett.80.4450
Likos C. N., Soft Matter, 2006, 2, 478–498. DOI: https://doi.org/10.1039/b601916c
Likos C. N., Watzlawek M., Löwen H., Phys. Rev. E, 1998, 58, 3135–3144. DOI: https://doi.org/10.1103/PhysRevE.58.3135
Lang A., Likos C. N., Watzlawek M., Löwen H., J. Phys.: Condens. Matter, 2000, 12, No. 24, 5087. DOI: https://doi.org/10.1088/0953-8984/12/24/302
Mladek B. M., Gottwald D., Kahl G., Neumann M., Likos C. N., Phys. Rev. Lett., 2006, 96, 045701. DOI: https://doi.org/10.1103/PhysRevLett.96.045701
Mladek B. M., Charbonneau P., Frenkel D., Phys. Rev. Lett., 2007, 99, 235702. DOI: https://doi.org/10.1103/PhysRevLett.99.235702
Lenz D. A., Mladek B. M., Likos C. N., Kahl G., Blaak R., J. Phys. Chem. B, 2010, 115, No. 22, 7218–7226. DOI: https://doi.org/10.1021/jp109132m
Neuhaus T., Likos C. N., J. Phys.: Condens. Matter, 2011, 23, No. 23, 234112. DOI: https://doi.org/10.1088/0953-8984/23/23/234112
Wilding N. B., Sollich P., Europhys. Lett., 2013, 101, No. 1, 10004. DOI: https://doi.org/10.1209/0295-5075/101/10004
Wilding N. B., Sollich P., J. Chem. Phys., 2014, 141, No. 9, 094903. DOI: https://doi.org/10.1063/1.4894374
Prestipino S., Phys. Rev. E, 2014, 90, 042306. DOI: https://doi.org/10.1103/PhysRevE.90.042306
Prestipino S., Gazzillo D., Tasinato N., Phys. Rev. E, 2015, 92, 022138. DOI: https://doi.org/10.1103/PhysRevE.92.022138
de Mello M., Díaz-Méndez R., Mendoza-Coto A., Entropy, 2023, 25, No. 2. DOI: https://doi.org/10.3390/e25020356
Baxter R. J., Exactly Solved Models in Statistical Mechanics, Academic Press, London, 1982.
Friedli S., Velenik Y., Statistical Mechanics of Lattice Systems. A Concrete Mathematical Introduction, Cambridge University Press, Cambridge, 2017. DOI: https://doi.org/10.1017/9781316882603
Finken R., Hansen J.-P., Louis A. A., J. Phys. A: Math. Gen., 2004, 37, No. 3, 577–590. DOI: https://doi.org/10.1088/0305-4470/37/3/003
Frydel D., Levin Y., Phys. Rev. E, 2018, 98, 062123. DOI: https://doi.org/10.1103/PhysRevE.98.062123
Frydel D., Levin Y., Phys. Rev. E, 2020, 102, 032101. DOI: https://doi.org/10.1103/PhysRevE.102.032101
Kozitsky Yu. V., Kozlovskii M. P., Dobush O. A., Condens. Matter Phys., 2020, 23, No. 2, 23502. DOI: https://doi.org/10.5488/CMP.23.23502
Kozlovskii M. P., Dobush O. A., J. Mol. Liq., 2022, 353, 118843. DOI: https://doi.org/10.1016/j.molliq.2022.118843
Romanik R. V., Dobush O. A., Kozlovskii M. P., Pylyuk I. V., Shpot M. A., J. Stat. Phys., 2026, 193, No. 14. DOI: https://doi.org/10.1007/s10955-026-03568-4
Liu W., Yan Z., Zhou G., Eur. Phys. J. B, 2021, 94, No. 6, 133. DOI: https://doi.org/10.1140/epjb/s10051-021-00142-7
Blume M., Phys. Rev., 1966, 141, 517–524. DOI: https://doi.org/10.1103/PhysRev.141.517
Capel H. W., Physica, 1966, 32, No. 5, 966–988. DOI: https://doi.org/10.1016/0031-8914(66)90027-9
Lee T. D., Yang C. N., Phys. Rev., 1952, 87, 410–419. DOI: https://doi.org/10.1103/PhysRev.87.410
Honchar Yu., Krasnytska M., Berche B., Holovatch Yu., Kenna R., Low Temp. Phys., 2025, 51, No. 5, 567–577. DOI: https://doi.org/10.1063/10.0036500
Stanley H. E., Introduction to Phase Transitions and Critical Phenomena, Oxford University Press, Oxford, 1971.
Romanik R. V., Dobush O. A., Kozlovskii M. P., Pylyuk I. V., Shpot M. A., Eur. Phys. J. B, 2026, 99, No. 13. DOI: https://doi.org/10.1140/epjb/s10051-026-01119-0
Mancini F., Eur. Phys. J. B, 2005, 47, No. 4, 527–540. DOI: https://doi.org/10.1140/epjb/e2005-00357-2
Fisher M. E., Ruelle D., J. Math. Phys., 1966, 7, No. 2, 260–270. DOI: https://doi.org/10.1063/1.1704928
Heyes D. M., Rickayzen G., J. Phys.: Condens. Matter, 2007, 19, No. 41, 416101. DOI: https://doi.org/10.1088/0953-8984/19/41/416101
Bender C. M., Orszag S. A., Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer Science & Business Media, New York, 1999. DOI: https://doi.org/10.1007/978-1-4757-3069-2_7
Dobush O. A., Kozlovskii M. P., Pylyuk I. V., Romanik R. V., Shpot M. A., The cell fluid model with Curie-Weiss interactions: special cases and analytical results, 2026. DOI: https://doi.org/10.1140/epjb/s10051-026-01235-x
Jain A. K., Landau D. P., Phys. Rev. B, 1980, 22, No. 1, 445–452. DOI: https://doi.org/10.1103/PhysRevB.22.445
Grollau S., Kierlik E., Rosinberg M. L., Tarjus G., Phys. Rev. E, 2001, 63, No. 4, 041111. DOI: https://doi.org/10.1103/PhysRevE.63.041111
Dobush O. A., Kozlovskii M. P., Pylyuk I. V., Plevachuk Y. O., Physica A, 2026, 681, 131133. DOI: https://doi.org/10.1016/j.physa.2025.131133
Kozlovskii M. P., Dobush O. A., Pylyuk I. V., Romanik R. V., Shpot M. A., Physica A, 2026, 692, 131510. DOI: https://doi.org/10.1016/j.physa.2026.131510
Franzese G., J. Mol. Liq., 2007, 136, No. 3, 267–273. DOI: https://doi.org/10.1016/j.molliq.2007.08.021
Louis A. A., Bolhuis P. G., Hansen J. P., Phys. Rev. E, 2000, 62, 7961–7972. DOI: https://doi.org/10.1103/PhysRevE.62.7961
Katayama Y., Mizutani T., Utsumi W., Shimomura O., Yamakata M., Funakoshi K.-i., Nature, 2000, 403, 170–173. DOI: https://doi.org/10.1038/35003143
Monaco G., Falconi S., Crichton W. A., Mezouar M., Phys. Rev. Lett., 2003, 90, 255701. DOI: https://doi.org/10.1103/PhysRevLett.90.255701
Yang M., Karmakar T., Parrinello M., Phys. Rev. Lett., 2021, 127, 080603. DOI: https://doi.org/10.1103/PhysRevLett.127.080603
Kurita R., Tanaka H., Science, 2004, 306, No. 5697, 845–848. DOI: https://doi.org/10.1126/science.1103073
de Oliveira A. B., Netz P. A., Colla T., Barbosa M. C., J. Chem. Phys., 2006, 124, No. 8, 084505.
Romanik R. V., Dobush O. A., Kozlovskii M. P., Pylyuk I. V., Shpot M. A., Ukr. J. Phys., 2026, 71, No. 8, 663. DOI: https://doi.org/10.15407/ujpe71.8.663
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