TITLE:
Equivalence Transformations among Ising Models
AUTHORS:
Yougang Feng
KEYWORDS:
Ising, Critical Point, Fractal, Equivalence Transformation
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.1,
January
14,
2015
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.