  We show that it is possible to determine the locus of Fisher zeroes in the
thermodynamic limit for the Ising model on planar (``fat'') phi4 random graphs
and their dual quadrangulations by matching up the real part of the high and
low temperature branches of the expression for the free energy. The form of
this expression for the free energy also means that series expansion results
for the zeroes may be obtained with rather less effort than might appear
necessary at first sight by simply reverting the series expansion of a function
g(z) which appears in the solution and taking a logarithm.
  Unlike regular 2D lattices where numerous unphysical critical points exist
with non-standard exponents, the Ising model on planar phi4 graphs displays
only the physical transition at c = exp (- 2 beta) = 1/4 and a mirror
transition at c=-1/4 both with KPZ/DDK exponents (alpha = -1, beta = 1/2, gamma
= 2). The relation between the phi4 locus and that of the dual quadrangulations
is akin to that between the (regular) triangular and honeycomb lattices since
there is no self-duality.
