,
The free energies of six-vertex models and the $n$-equivalence relation
Abstract Book of the XXIII IUPAP International Conference on Statistical Physics, Genova, Italy, (9-13 July 2007)
Аннотация
The free energies of six-vertex models
on general domain $D$
with various boundary conditions
are investigated with the use of the $n$-equivalence relation
which classifies the thermodynamic limit properties.
It is derived
that the free energy of the model on the rectangle is unique
in the limit where (height, width) both go to infinity.
It is derived
that the free energies of the model on $D$ are classified
through the densities of left/down arrows on the boundary.
Specifically
the free energy
is identical to that obtained
by Lieb and Sutherland with the cyclic boundary condition
when the densities are both equal to $1/2$.
This fact explains several results
already obtained through the transfer matrix calculations.
The relation to the domino tiling (or dimer, or matching) problems
are also noted.
The graph-directed IFS fractal structure of the six-vertex model
and its relations to the thermodynamic limit properties will be explained.\\
1) Kazuhiko Minami: J.Phys.Soc.Jpn.74 (2005) 1640-1641\\
2) Kazuhiko Minami: cond-mat/0607513\\
3) http://www.math.nagoya-u.ac.jp/~minami/index.html
