Further evidence that the transition of 4D dynamical triangulation is 1st order

Abstract

We confirm recent claims that, contrary to what was generally believed, the phase transition of the dynamical triangulation model of four-dimensional quantum gravity is of first order. We have looked at this at a volume of 64, 000 four-simplices, where the evidence in the form of a double peak histogram of the action is quite clear.

The effective action in 4-dim CDT. The transfer matrix approach

“…The weak gravity phase was dominated by the branched polymer geometries with a Hausdorff dimension d H = 2 and the strong gravity phase by collapsed geometries with possibly d H = ∞, corresponding to universes without a linear extension. The two phases were separated by a first order phase transition [22][23][24].…”

The transfer matrix in four-dimensional CDT

“…In higher dimensions DT was studied numerically, using Monte Carlo simulations both in three dimensions [35][36][37][38][39] and four dimensions [40,41]. However, no convincing continuum limit has been obtained so far in higher dimensions [42][43][44], and this was one of the motivations for changing the class of triangulations used in the path integral in CDT. 2 In the CDT formalism one sums over geometries with a (proper) time foliation.…”

Exploring the Phase Diagram for Lattice Quantum Gravity

“…It is well established in the literature [13] that, at the point β = 0, along the critical line AB, there is a first order phase transition for combinatorial triangulations, and Ref. [17] provides evidence that this is also true for degenerate triangulations.…”

“…The solid line AB dividing the extended and branched polymer phases has been extensively studied in the literature at the point β = 0. At that point the transition is almost certaintly first order [13,14]. The dashed line CD appears to be much softer than the AB transition and appears to be a cross-over seperating the collapsed and extended regions of a single phase.…”