  We show that for 1+1 dimensional Causal Dynamical Triangulations (CDT)
coupled to 4 massive scalar fields one can construct an effective transfer
matrix if the masses squared is larger than or equal to 0.05. The properties of
this transfer matrix can explain why CDT coupled to matter can behave
completely different from "pure" CDT. We identify the important critical
exponent in the effective action, which may determine the universality class of
the model.
