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A second-order phase transition in CDT

J. Ambjorn, S. Jordan, J. Jurkiewicz, R. Loll

TL;DR

Ambjørn et al. address the nonperturbative quantization of gravity using four‑dimensional Causal Dynamical Triangulations (CDT) and investigate whether a continuum limit can be defined via a second‑order phase transition. They map the CDT phase diagram and study the B‑C transition with finite‑size scaling and Binder cumulants to determine its order. They report a second‑order transition with a shift exponent $\tilde{\nu} = 2.51(3)$ and Binder cumulants tending to zero, contrasting with indications of a first‑order A‑C transition. This provides strong evidence for a viable continuum limit in 4D CDT and motivates exploring critical phenomena and possible connections to the asymptotic safety program in quantum gravity.

Abstract

Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.

A second-order phase transition in CDT

TL;DR

Ambjørn et al. address the nonperturbative quantization of gravity using four‑dimensional Causal Dynamical Triangulations (CDT) and investigate whether a continuum limit can be defined via a second‑order phase transition. They map the CDT phase diagram and study the B‑C transition with finite‑size scaling and Binder cumulants to determine its order. They report a second‑order transition with a shift exponent and Binder cumulants tending to zero, contrasting with indications of a first‑order A‑C transition. This provides strong evidence for a viable continuum limit in 4D CDT and motivates exploring critical phenomena and possible connections to the asymptotic safety program in quantum gravity.

Abstract

Causal Dynamical Triangulations (CDT) are a concrete attempt to define a nonperturbative path integral for quantum gravity. We present strong evidence that the lattice theory has a second-order phase transition line, which can potentially be used to define a continuum limit in the conventional sense of nongravitational lattice theories.

Paper Structure

This paper contains 5 sections, 6 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Causal Dynamical Triangulations
  3. The phase diagram of CDT
  4. The order of the B-C phase transition
  5. Discussion

Figures (3)

  • Figure 1: The phase diagram of CDT. The large crosses represent actual measurements.
  • Figure 2: Measuring the location $\Delta^c$ of B-C transition points at $\kappa_0=2.2$ for different system sizes $N_4$ to determine the shift exponent $\tilde{\nu}$.
  • Figure 3: Dependence of the minimum of the Binder cumulant $B_{\mathrm{conj}(\Delta)}$ on the (inverse) system size at the B-C transition. At a second-order transition, $B^{\min}\!\rightarrow\! 0$ in the infinite-volume limit. (Fit excludes the two points on the right.)