Georgii H.O., Higuchi Y.
Percolation and number of phases in the 2D Ising 
model
(62K, LaTeX)

ABSTRACT.  We reconsider the percolation approach of Russo, Aizenman and Higuchi 
for showing that there exist only two phases in the Ising model on the 
square lattice. 
We give a fairly short alternative proof which is only based on FKG 
monotonicity and avoids the use of GKS-type inequalities 
originally needed for some background results. Our proof extends to 
the Ising model on other planar lattices such as the triangular 
and honeycomb lattice. 
We can also treat the Ising antiferromagnet in an external field and 
the hard-core lattice gas model on $Z^2$.