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Elementary Excitations of Ising Models at the Critical Temperatures

Received: 8 October 2014     Accepted: 23 October 2014     Published: 30 October 2014
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Abstract

Ordered Ising models as ferromagnetic having nonsingular heat capacities at the critical temperatures are considered. A new parameter vector q ⃗ is found to describe the spin correlations and fluctuation characteristics. The conservation of scalar q indicates that there is simple harmonic motion of q ⃗, and the motion’s quantum is called block-spin phonons, like the phonons in a crystal, resulting in nonsingular heat capacity near the critical point. The harmonic motion shows there are hierarchies and symmetries of fluctuations, while the soft mode may lead to the interactions of block-spin phonons with different frequencies. We are certain that the critical point for an Ising model only exists in a statistical sense although the system at the critical temperature. The fluctuations undergo about the critical point, which the system never attains. It is the first time for us that the specific forms of the spins’ correlation functions for Ising models at the critical temperatures are obtained.

Published in American Journal of Modern Physics (Volume 3, Issue 6)
DOI 10.11648/j.ajmp.20140306.11
Page(s) 211-217
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Ising, Correlation, Phonon, Heat Capacity, Fluctuation

References
[1] Freeman. J. Dyson, 1956 General theory of spin-wave interactions. Phys. Rev. 102, 1217-1230.
[2] V. G. Vaks, A. L. Larkin, and S. A. Pikin, 1968 Spin waves and correlation functions in a ferromagnetic. Soviet Physics, JETP. 26, March, 647.
[3] Arthur E. Ferdinand and Michael E. Fisher, 1969 Bounded and inhomogeneous Ising models. I. Specific-heat anomaly of a finite lattice. Phys. Rev. 185, 832-846.
[4] J. M. Radcliffe, 1971 Some properties of coherent spin states. J. Phys. A: Gen. Phys; 4, 313-323.
[5] You-gang Feng 2011 arxiv:1111.2233
[6] You-Gang Feng, 2014 Self-similar transformations of lattice-Ising models at critical temperatures. Amer. J. Mod. Phys. 3(4), 184-194.
[7] You-Gang Feng, 2014 Secondary phase transition of Ising model. Amer. J. Mod. Phys. 3(4), 178-183.
[8] Charles Kittel, 1996 Introduction to solid state physics. 7th Edition, John&Wiley Sons Ltd., New York.
[9] G. Delfino and G. Mussardo, 1995 The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at . Nucl. Phys. B455, 724-758.
[10] Grag A. Tracy and Barry M. McCoy, 1973 Neutron scattering and the correlation functions of the Ising model near . Phys. Rev. Lett. 31, 1500-1504.
[11] G. Nicolis and Ilya. Prigogine, 1977 Self-organization in nonequilibrium system: from dissipative structures to order through fluctuations, John&Wiley Sons Ltd., New York.
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  • APA Style

    You-Gang Feng. (2014). Elementary Excitations of Ising Models at the Critical Temperatures. American Journal of Modern Physics, 3(6), 211-217. https://doi.org/10.11648/j.ajmp.20140306.11

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    ACS Style

    You-Gang Feng. Elementary Excitations of Ising Models at the Critical Temperatures. Am. J. Mod. Phys. 2014, 3(6), 211-217. doi: 10.11648/j.ajmp.20140306.11

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    AMA Style

    You-Gang Feng. Elementary Excitations of Ising Models at the Critical Temperatures. Am J Mod Phys. 2014;3(6):211-217. doi: 10.11648/j.ajmp.20140306.11

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  • @article{10.11648/j.ajmp.20140306.11,
      author = {You-Gang Feng},
      title = {Elementary Excitations of Ising Models at the Critical Temperatures},
      journal = {American Journal of Modern Physics},
      volume = {3},
      number = {6},
      pages = {211-217},
      doi = {10.11648/j.ajmp.20140306.11},
      url = {https://doi.org/10.11648/j.ajmp.20140306.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20140306.11},
      abstract = {Ordered Ising models as ferromagnetic having nonsingular heat capacities at the critical temperatures are considered. A new parameter vector q ⃗ is found to describe the spin correlations and fluctuation characteristics. The conservation of scalar q indicates that there is simple harmonic motion of q ⃗, and the motion’s quantum is called block-spin phonons, like the phonons in a crystal, resulting in nonsingular heat capacity near the critical point. The harmonic motion shows there are hierarchies and symmetries of fluctuations, while the soft mode may lead to the interactions of block-spin phonons with different frequencies. We are certain that the critical point for an Ising model only exists in a statistical sense although the system at the critical temperature. The fluctuations undergo about the critical point, which the system never attains. It is the first time for us that the specific forms of the spins’ correlation functions for Ising models at the critical temperatures are obtained.},
     year = {2014}
    }
    

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  • TY  - JOUR
    T1  - Elementary Excitations of Ising Models at the Critical Temperatures
    AU  - You-Gang Feng
    Y1  - 2014/10/30
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajmp.20140306.11
    DO  - 10.11648/j.ajmp.20140306.11
    T2  - American Journal of Modern Physics
    JF  - American Journal of Modern Physics
    JO  - American Journal of Modern Physics
    SP  - 211
    EP  - 217
    PB  - Science Publishing Group
    SN  - 2326-8891
    UR  - https://doi.org/10.11648/j.ajmp.20140306.11
    AB  - Ordered Ising models as ferromagnetic having nonsingular heat capacities at the critical temperatures are considered. A new parameter vector q ⃗ is found to describe the spin correlations and fluctuation characteristics. The conservation of scalar q indicates that there is simple harmonic motion of q ⃗, and the motion’s quantum is called block-spin phonons, like the phonons in a crystal, resulting in nonsingular heat capacity near the critical point. The harmonic motion shows there are hierarchies and symmetries of fluctuations, while the soft mode may lead to the interactions of block-spin phonons with different frequencies. We are certain that the critical point for an Ising model only exists in a statistical sense although the system at the critical temperature. The fluctuations undergo about the critical point, which the system never attains. It is the first time for us that the specific forms of the spins’ correlation functions for Ising models at the critical temperatures are obtained.
    VL  - 3
    IS  - 6
    ER  - 

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Author Information
  • College of Science, Guizhou University, Huaxi, Guiyang, 550025 China

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