M.Biskup, L.Chayes, R. Kotecky'
On the Continuity of the Magnetization 
and the Energy Density for Potts Models 
on Two-dimensional Graphs 
(41K, AMS-TeX)

ABSTRACT.  We consider the $q$-state Potts model on two-dimensional 
planar graphs. Our only assumptions concerning the graph and 
interaction are that the associated graphical representations 
satisfy the conclusion of the theorem of Gandolfi, Keane and Russo 
\cite{GKR}. In addition to $\Bbb Z^2$, the class of graphs we 
consider contains, for example, the triangular, honeycomb, and 
Kagom\'e lattices. Under these conditions 
we show that the only possible point of discontinuity of the 
magnetization and the energy density is at the onset of the 
magnetic ordering transition (i.e., at the threshold for bond 
percolation in the random-cluster model). The result generalizes 
to any model with a natural dual, appropriate FKG monotonicity 
properties and a percolation characterization of the Gibbs 
uniqueness.