Finite size scaling in 2d causal set quantum gravity.

Abstract

We study the dependence on size, N, of 2d causal set quantum gravity. This theory is known to exhibit a phase transition as the analytic continuation parameter β, akin to an inverse temperature, is varied. Using a scaling analysis we find that the asymptotic regime is reached at relatively small values of N. Focussing on the \newcommand{\twod}{2d} \twod causal set action S, we find that \newcommand{\av}[1]< #1 > \newcommand{\ep}ε \newcommand{\e}{e} \newcommand{\be}{\barε} β \av{S} scales like N^ν where the scaling exponent ν takes different values on either side of the phase transition. For \newcommand{\ep}ε \newcommand{\e}{e} \newcommand{\be}{\barε} β > βc we find that ν=2 which is consistent with our analytic predictions for a non-continuum phase in the large β regime. For \newcommand{\ep}ε \newcommand{\e}{e} \newcommand{\be}{\barε} β<βc we find that ν=0 , consistent with a continuum phase of constant negative curvature thus suggesting a dynamically generated cosmological constant. Moreover, we find strong evidence that the phase transition is first order. Our results strongly suggest that the asymptotic regime is reached in \newcommand{\twod}{2d} \twod causal set quantum gravity for N ≳ 65 .