Multicanonical simulation of 3D dynamical triangulation model and a new phase structure

Abstract

We apply the multicanonical technique to the three dimensional dynamical triangulation model, which is known to exhibit a first order phase transition with the Einstein-Hilbert action. We first clarify the first order nature of the phase transition with the Einstein-Hilbert action in several ways including a high precision finite size scaling analysis. We then add a new local term to the action and confirm the conjecture made through the MCRG technique that the line of the first order phase transition extends to the expanded phase diagram, ending at a point. Fractal dimension at the end point is measured to be around three up to the present size.