Ising model in the Rényi statistics: the finite size effects
DOI:
https://doi.org/10.5488/cmp.27.43603Keywords:
Rényi statistics, microcanocical ensemble, entropic phase transition, Ising modelAbstract
The Rényi statistics is applied for a description of finite size effects in the 1D Ising model.We calculate the internal energy of the spin chain and the system temperature using the Rényi distribution and postulate them to be equal to their counterparts, obtained in the microcanonical ensemble. It allows us to self-consistently derive the Rényi q-index and the Lagrange parameter T to relate them to the physically observed system temperature Tph, and to show that the entropic phase transitions are possible in a broad temperature domain. We have also studied the temperature dependence of the internal energy U(Tph) at constant q and an influence of the size related effects on the system thermodynamics.
References
Jaynes E. T., Phys. Rev., 1957, 106, 620. DOI: https://doi.org/10.1103/PhysRev.106.620
Ho W., J. Chem. Phys., 2002, 117, 11033. DOI: https://doi.org/10.1063/1.1521153
Claridge S. A., Schwartz J. J., Weiss P. S, ACS Nano, 2011, 5, 693–729. DOI: https://doi.org/10.1021/nn103298x
Jarzynski C., Thermodynamics of Nanosystems, In: Reports on Leading-Edge Engineering from the 2003 NAE Symposium on Frontiers of Engineering, National Academies Press, Washington, D. C., 2004.
Jarzynski C., Equalities and Inequalities: Irreversibility and the Second Law of Thermodynamics at the Nanoscale. In: Duplantier B. (Eds.), Progress in Mathematical Physics, 63, Birkhäuser, Basel, 2013. DOI: https://doi.org/10.1007/978-3-0348-0359-5_4
Zubarev D. N., Morozov V. G., Röpke G., Statistical Mechanics of Nonequilibrium Processes, Vol. 1, Basic Concepts, Kinetic theory, Akademie Verlag, Berlin, 1996.
Esposito M., Gaspard P., Phys. Rev. E, 2007, 76, 041134. DOI: https://doi.org/10.1103/PhysRevE.76.041134
Riera-Campeny A., Sanpera A., Strasberg P., Phys. Rev. E, 2022, 105, 054119. DOI: https://doi.org/10.1103/PhysRevE.105.054119
Turán P. (Ed.), Selected papers of Alfréd Rényi, Vol. 2, Akadémiai Kiadó, Budapest, 1976.
Tsallis C., J. Stat. Phys., 1988, 52, 479–487. DOI: https://doi.org/10.1007/BF01016429
Tsallis C., Entropy, 2019, 21, 696. DOI: https://doi.org/10.3390/e21070696
Sharma B. D., Mittal D. P., J. Math. Sci., 1975, 10, 28-40. DOI: https://doi.org/10.1080/00087114.1975.10796605
Abe S., Phys. Lett. A, 2000, 271, 74. DOI: https://doi.org/10.1016/S0375-9601(00)00337-6
Bashkirov A. G., In: Chaos, Nonlinearity, Complexity, Vol. 206, Sengupta A. (Ed.), Springer Berlin Heidelberg, Berlin, Heidelberg, 2006, 114–161.
Almeida M. P., Physica A, 2001, 300, 424–432. DOI: https://doi.org/10.1016/S0378-4371(01)00353-3
Klimontovich Yu. L., Statistical Theory of Open Systems: Volume 1: A Unified Approach to Kinetic Description of Processes in Active Systems, Fundamental Theories of Physics, Vol. 67, Springer Netherlands, Dordrecht, 1995.
Morozov V. G., Mathey S., Röpke G., Phys. Rev. A, 2012, 85, 022101. DOI: https://doi.org/10.1103/PhysRevA.85.022101
Ignatyuk V. V., Morozov V. G., Phys. Rev. A, 2015, 91, 052102. DOI: https://doi.org/10.1103/PhysRevA.91.052102
Semin V., Petruccione F., Sci. Rep., 2020, 10, 2607. DOI: https://doi.org/10.1038/s41598-020-59241-7
Parvan A. S., Biró T. S., Phys. Lett. A, 2005, 340, 375–387. DOI: https://doi.org/10.1016/j.physleta.2005.04.036
Parvan A. S., Phys. Lett. A, 2006, 360, 26–34. DOI: https://doi.org/10.1016/j.physleta.2006.07.052
Parvan A. S., Biró T. S., Phys. Lett. A, 2010, 374, 1951–1957. DOI: https://doi.org/10.1016/j.physleta.2010.03.007
Landau L. D., Lifshits E. M., Statistical Physics, Course of Theoretical Physics, Vol. 5, Elsevier, third edn., 2013.
Lenzi E. K., Mendes R. S., da Silva L. R., Physica A, 2000, 280, 337–345. DOI: https://doi.org/10.1016/S0378-4371(00)00007-8
Tsallis C., Mendes R. S., Plastino A. R., 1998, Physica, 261, 534–554. DOI: https://doi.org/10.1016/S0378-4371(98)00437-3
Chung W. S., Hassanabadi H., Physica A, 2019, 532, 121720. DOI: https://doi.org/10.1016/j.physa.2019.121720
Ilin P. K., Koval G. V., Savchenko A. M., Moscow Univ. Phys., 2020, 75, No. 5, 415–419. DOI: https://doi.org/10.3103/S0027134920050148
Tsallis C., Axioms, 2016, 5, 20. DOI: https://doi.org/10.3390/axioms5030020
Ruthotto E., Preprint arXiv:cond-mat.stat-mech/0310413, 2003.
Ishihara M., Eur. Phys. J. B, 2022, 95, 53. DOI: https://doi.org/10.1140/epjb/s10051-022-00309-w
Ishihara M., Eur. Phys. J. B, 2023, 96, 13. DOI: https://doi.org/10.1140/epjb/s10051-023-00481-7
Lima A. R., Penna T. J. P., Phys. Lett. A, 1999, 256, 221. DOI: https://doi.org/10.1016/S0375-9601(99)00241-8
Campisi M., Zueco D., Talkner P., Chem. Phys., 2010, 375, 187–194. DOI: https://doi.org/10.1016/j.chemphys.2010.04.026
Ramshaw J. D., Phys. Lett. A, 1995, 198, 122–125. DOI: https://doi.org/10.1016/0375-9601(95)00033-Y
Prosper H. B., Am. J. Phys., 1993, 61, 54. DOI: https://doi.org/10.1119/1.17410
Downloads
Published
License
Copyright (c) 2024 V. V. Ignatyuk, A. P. Moina
This work is licensed under a Creative Commons Attribution 4.0 International License.