Z_2-Regge versus Standard Regge Calculus in two dimensions

Details Z_2-Regge versus Standard Regge Calculus in two dimensions Z_2-Regge versus Standard Regge Calculus in two dimensions

1999-03-16

arxiv.org/abs/hep-lat/9903028v1

Phys.Rev. D59 (1999) 124018

Physics

High Energy Physics

High Energy Physics - Lattice

21 pages, 16 ps-figures, to be published in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.59.124018

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 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.

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