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

Abstract

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 β, μ > 0 where the infinite-volume free energy converges, yielding results on the convergence and asymptotic properties of the partition function and the Gibbs measure.