Finite size scaling in 2d causal set quantum gravity

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 beta, 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 2d causal set action S, we find that beta < S > scales like N-nu where the scaling exponent nu takes different values on either side of the phase transition. For beta > beta(c) we find that nu = 2 which is consistent with our analytic predictions for a non-continuum phase in the large beta regime. For beta < beta(c) we find that nu = 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 2d causal set quantum gravity for N greater than or similar to 65.