Z2-Regge versus standard Regge calculus in two dimensions - Bittner, Elmar; Hauke, A.; Holm, Christian; Janke, Wolfhard; Markum, Harald; Riedler, Jürgen (Physical review. D, Particles, fields, gravitation, and cosmology, 1999)
We consider two versions of quantum Regge calculus: the standard Regge calculus where the quadratic link lengths of the simplicial manifold vary continuously and the Z2 Regge model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible Z2 model still retains the universal characteristics of standard Regge theory in two dimensions. In order to compare observables such as the average curvature or Liouville field susceptibility, we use in both models the same functional integration measure, which is chosen to render the Z2 Regge model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the Z2 Regge model is analyzed by mean-field theory.
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