Equivalence Transformations among Ising Models

Yougang Feng^*

Guizhou University, Guiyang, China.

DOI: 10.4236/jmp.2015.61003                

Abstract

Using topology, fractal analysis and investigation of lattice formation process we find two types of equivalence transformations among Ising models: topological equivalence transformation and formation equivalence transformation. With the help of the transformations and the known data of the critical points of simple cubic (sc) lattice and planar square (sq) lattice we get directly the critical points for face-centered cubic (fcc) lattice, body-centered cubic (bcc) lattice and diamond (d) lattice. The transformation itself results no error in the calculation. Other than Monte Carlo method and series expansion approach the equivalence transformations help us simplify much more greatly the calculation of the critical points for the three-dimensional models and understand much more deeply the structural connection among Ising models.

Keywords

Ising, Critical Point, Fractal, Equivalence Transformation

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Liu, S.H. (1986) Solid State Physics, 39, 207-273. http://dx.doi.org/10.1016/S0081-1947(08)60370-7
[2]	Havlin, S. and Ben-Avraham, D. (1987) Advances in Physics, 36, 695-798. http://dx.doi.org/10.1080/00018738700101072
[3]	Feng, Y.-G. (2014) American Journal of Modern Physics, 3, 184-194. http://dx.doi.org/10.11648/j.ajmp.20140304.16
[4]	Feng, Y.-G. (2014) American Journal of Modern Physics, 3, 178-183. http://dx.doi.org/10.11648/j.ajmp.20140304.15
[5]	Feng, Y.-G. (2014) American Journal of Modern Physics, 3, 211-217. http://dx.doi.org/10.11648/j.ajmp.20140306.11
[6]	Kramers, H.A. and Wannier, G.H. (1941) Physical Review, 60, 252-262. http://dx.doi.org/10.1103/PhysRev.60.252
[7]	Onsager, L. (1944) Physical Review, 65, 117-149. http://dx.doi.org/10.1103/PhysRev.65.117
[8]	Fisher, M.E. (1968) Physical Review, 113, 969-981. http://dx.doi.org/10.1103/PhysRev.113.969
[9]	Schiff, L.I. (1968) Quantum Mechanics. 3rd Edition, McGraw-Hill, New York.
[10]	Fulton, W. (1995) Algebraic Topology. Springer-Verlag, New York. http://dx.doi.org/10.1007/978-1-4612-4180-5
[11]	Kittel, C. (2005) Introduction to Solid State Physics. John Willey & Sons, New York.
[12]	Lundow, P.H., Markstrom, K. and Rosengren, A. (2009) Philosophical Magazine, 89, 2009-2042. http://dx.doi.org/10.1080/14786430802680512
[13]	Sykes, M.F., Gaunt, D.S., Roberts, P.D. and Wyles, J.A. (1972) Journal of Physics A: General Physics, 5, 640-652. http://dx.doi.org/10.1088/0305-4470/5/5/005
[14]	Domb, C. (1974) Ising Model. In: Domb, C. and Green, M.S., Eds., Phase Transitions and Critical Phenomena, Vol. 3, Academic Press, London, 357-484.
[15]	Mouritsen, O.G. (1980) Journal of Physics C: Solid State Physics, 13, 3909. http://dx.doi.org/10.1088/0022-3719/13/20/013
[16]	Deng, Y.J. and Blote, H.W.J. (2003) Physical Review E, 68, Article ID: 036125. http://dx.doi.org/10.1103/PhysRevE.68.036125
[17]	Feng, Y.G. (2005) Electronic Journal of Theoretical Physics, 7, 12-18.
[18]	Wannier, G.H. (1945) Reviews of Modern Physics, 17, 50-60. http://dx.doi.org/10.1103/RevModPhys.17.50