3.5 Influence of the measure

For the pure Einstein action, (12View Equation) with λ = 0, some differences between the M1 = dl∕l- and the M2 = ldl-measure were investigated on a 44-lattice by Beirl et al. [2930]. A constant-volume constraint was used for simulations with the M1-measure, and a cutoff l2 < const for M2. A study of the k-dependence of bulk geometric quantities agreed with previous simulations, wherever applicable. For small k, both measures lead essentially to identical results. For the M1-measure only, one finds that ⟨R ⟩∕⟨V ⟩ and ⟨A ⟩ exhibit a jump at some k0, due to the formation of spikes (isolated long link lengths, with the areas staying small). From this, and the study of edge length distributions, one concludes that the DeWitt-type measure M2 is generally better behaved.
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