We discuss the relationship between the phase diagram of the Q=0 state Potts
model, the arboreal gas model, and the supersphere sigma model S^{0,2} =
OSP(1/2) / OSP(0/2). We identify the Potts antiferromagnetic critical point
with the critical point of the arboreal gas (at negative tree fugacity), and
with a critical point of the sigma model. We show that the corresponding
conformal theory on the square lattice has a non-linearly realized OSP(2/2) =
SL(1/2) symmetry, and involves non-compact degrees of freedom, with a
continuous spectrum of critical exponents. The role of global topological
properties in the sigma model transition is discussed in terms of a generalized
arboreal gas model.Comment: 23 pages, 4 figure
