6533b835fe1ef96bd129fe1d

RESEARCH PRODUCT

Z2-Regge versus standard Regge calculus in two dimensions

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description

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 ${Z}_{2}$ Regge model where they are restricted to two possible values. The goal is to determine whether the computationally more easily accessible ${Z}_{2}$ 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 ${Z}_{2}$ Regge model particularly simple. Expectation values are computed numerically and agree qualitatively for positive bare couplings. The phase transition within the ${Z}_{2}$ Regge model is analyzed by mean-field theory.