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We introduce a transfer matrix formalism for the (annealed) Ising modelcoupled to two-dimensional causal dynamical triangulations. Using theKrein-Rutman theory of positivity preserving operators we study severalproperties of the emerging transfer matrix. In particular, we determine regionsin the quadrant of parameters beta, mu >0 where the infinite-volume free energyconverges, yielding results on the convergence and asymptotic properties of thepartition function and the Gibbs measure.

Bounds on the critical line via transfer matrix methods for an Ising model coupled to causal dynamical triangulations