  We introduce a transfer matrix formalism for the (annealed) Ising model
coupled to two-dimensional causal dynamical triangulations. Using the
Krein-Rutman theory of positivity preserving operators we study several
properties of the emerging transfer matrix. In particular, we determine regions
in the quadrant of parameters beta, mu >0 where the infinite-volume free energy
converges, yielding results on the convergence and asymptotic properties of the
partition function and the Gibbs measure.
