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Zeroth order phase transition induced by ergodicity breaking in a mean-field system

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

A spin chain model with mean-field interactions is studied within the microcanonical ensemble. Under local microcanonical dynamics, gaps in the space of extensive variables can be open up leading to the ergodicity breaking of this system. As a consequence, our mean-field system can exhibit the zero-order phase transition accompanied with an entropy jump at the transition point. Moreover, the global phase diagram of the system is constructed.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data reported in the paper are available from the corresponding author on reasonable request.]

References

  1. M.W. Zemansky and R.H. Dittman, Heat and Thermodynamics: An Intermediate Textbook (McGraw-Hill, New York, 1997)

    Google Scholar 

  2. J. Barré, D. Mukamel, and S. Ruffo, Phys. Rev. Lett. 87, 030601 (2001)

    Article  ADS  Google Scholar 

  3. R. B. Frigori, L. G. Rizzi, and N. A. Alves, Eur. Phys. J. B 75, 311 (2010)

    Article  ADS  Google Scholar 

  4. V. V. Hovhannisyan, N. S. Ananikian, A. Campa, and S. Ruffo, Phys. Rev. E 96, 062103 (2017)

    Article  ADS  Google Scholar 

  5. V. V. Prasad, A. Campa, D. Mukamel, and S. Ruffo, Phys. Rev. E 100, 052135 (2019)

    Article  ADS  Google Scholar 

  6. T. Dauxois, S. Ruffo, M. Wilkens and E. Arimondo, Dynamics and Thermodynamics of Systems with Long-Range Interactions (Springer, New York, 2002)

    Book  Google Scholar 

  7. T. Dauxois, S. Ruffo and L. F. Cugliandolo, Long-Range Interacting Systems (Oxford University Press, Oxford, 2010)

    MATH  Google Scholar 

  8. J.-X. Hou, and X.-C. Yu, Mod. Phys. Lett. B 32, 1850053 (2018)

    Article  ADS  Google Scholar 

  9. Z.-Y. Yang, and J.-X. Hou, Mod. Phys. Lett. B 33, 1950072 (2019)

    Article  ADS  Google Scholar 

  10. Z.-Y. Yang, and J.-X. Hou, Eur. Phys. J. B 92, 170 (2019)

    Article  ADS  Google Scholar 

  11. J.-X. Hou, Phys. Rev. E 99, 052114 (2019)

    Article  ADS  Google Scholar 

  12. J.-X. Hou, X.-C. Yu, and J.-M. Hou, Int. J. Theor. Phys. 55, 3923–3926 (2016)

    Article  Google Scholar 

  13. J.-X. Hou, Eur. Phys. J. B 93, 82 (2020)

    Article  ADS  Google Scholar 

  14. D. Mukamel, S. Ruffo, and N. Schreiber, Phys. Rev. Lett. 95, 240604 (2005)

    Article  ADS  Google Scholar 

  15. Z.-Y. Yang, and J.-X. Hou, Phys. Rev. E 101, 052106 (2020)

    Article  ADS  Google Scholar 

  16. C. Hudson, Z. Phys. Chem. 47, 113 (1904)

    Google Scholar 

  17. T. Narayanan and A. Kumar, Phys. Rep. 249, 135 (1994)

    Article  ADS  Google Scholar 

  18. V. P. Maslov, Mathematical notes of the Academy of Sciences of the USSR 76, 697 (2004)

    Google Scholar 

  19. S. Gunasekaran, R. B. Mann, and D. Kubizňák, J. High Energy Phys. 2012, 110 (2012)

    Article  ADS  Google Scholar 

  20. N. Altamirano, D. Kubizňák, and R. B. Mann, Phys. Rev. D 88, 101502(R) (2013)

    Article  ADS  Google Scholar 

  21. N. Altamirano, D. Kubizňák, R. B. Mann, and Z. Sherkatghanad, Classical Quantum Gravity 31, 042001 (2014)

    Article  ADS  Google Scholar 

  22. S. W. Wei, P. Cheng, and Y. X. Liu, Phys. Rev. D 93, 084015 (2016)

    Article  MathSciNet  ADS  Google Scholar 

  23. A. M. Frassino, D. Kubizňák, R. B. Mann, and F. Simovic, J. High Energy Phys. 2014, 080 (2014)

    Article  Google Scholar 

  24. D.-C. Zou, Y. Liu, and B. Wang, Phys. Rev. D 90, 044063 (2014)

    Article  ADS  Google Scholar 

  25. M. B. Jahani-Poshteh, B. Mirza, Z. Sherkatghanad, Phys. Rev. D 88, 024005 (2013)

    Article  ADS  Google Scholar 

  26. R. A. Hennigar and R. B. Mann, Entropy 17, 8056 (2015)

    Article  ADS  Google Scholar 

  27. N. Altamirano, D. Kubizňák, R. B. Mann, and Z. Sherkatghanad, Galaxies 2, 89 (2014)

    Article  ADS  Google Scholar 

  28. D. Kubizňák and F. Simovic, Classical Quantum Gravity 33, 245001 (2016)

    Article  ADS  Google Scholar 

  29. A. Dehyadegari, A. Sheykhi, and A. Montakhab, Phys. Rev. D 96, 084012 (2017)

    Article  MathSciNet  ADS  Google Scholar 

  30. A. Dehyadegari and A. Sheykhi, Phys. Rev. D 98, 024011 (2018)

    Article  ADS  Google Scholar 

  31. P. Gaspard, J. Stat. Mech. 2012, P08021 (2012)

    Article  Google Scholar 

  32. M. Kac, G. E. Uhlenbeck, and P.C. Hemmer, J. Math. Phys. 4, 216–228 (1963)

    Article  ADS  Google Scholar 

  33. J.-X. Hou, Phys. Rev. E 102, 036101 (2020)

    Article  MathSciNet  ADS  Google Scholar 

  34. N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A.H. Teller, and E. Teller, J. Chem. Phys. 21, 1087 (1953)

    Article  ADS  Google Scholar 

  35. M. Creutz, Phys. Rev. Lett. 50, 1411 (1983)

    Article  MathSciNet  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Physics, Southeast University, Nanjing, 211189, Jiangsu, China

    Ji-Xuan Hou

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  1. Ji-Xuan Hou
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Contributions

Ji-Xuan Hou provided the idea, made all the computations and wrote the manuscript.

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Correspondence to Ji-Xuan Hou.

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Hou, JX. Zeroth order phase transition induced by ergodicity breaking in a mean-field system. Eur. Phys. J. B 94, 6 (2021). https://doi.org/10.1140/epjb/s10051-020-00025-3

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  • DOI: https://doi.org/10.1140/epjb/s10051-020-00025-3

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