Critical Behavior of Dynamically Triangulated Quantum Gravity in Four Dimensions

Abstract

We performed detailed study of the phase transition region in Four Dimensional Simplicial Quantum Gravity, using the dynamical triangulation approach. The phase transition between the Gravity and Antigravity phases turned out to be asymmetrical, so that we observed the scaling laws only when the Newton constant approached the critical value from perturbative side. The curvature susceptibility diverges with the scaling index $-.6$. The physical (i.e. measured with heavy particle propagation) Hausdorff dimension of the manifolds, which is 2.3 in the Gravity phase and 4.6 in the Antigravity phase, turned out to be 4 at the critical point, within the measurement accuracy. These facts indicate the existence of the continuum limit in Four Dimensional Euclidean Quantum Gravity.

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