Elementary Excitations of Ising Models at the Critical Temperatures

You-Gang Feng

doi:doi:10.11648/j.ajmp.20140306.11

| Peer-Reviewed

Elementary Excitations of Ising Models at the Critical Temperatures

You-Gang Feng

Published in American Journal of Modern Physics (Volume 3, Issue 6)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download

Author Information

You-Gang Feng

College of Science, Guizhou University, Huaxi, Guiyang, 550025 China

Download PDF

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

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  -

Copy | Download