Finite size scaling in 2d causal set quantum gravity
Bibliographic record
Abstract
Abstract We study the dependence on size, N , of 2 d 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mstyle> </mml:math> causal set action S , we find that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>β</mml:mi> <mml:mo stretchy="false">〈</mml:mo> <mml:mi>S</mml:mi> <mml:mo stretchy="false">〉</mml:mo> </mml:mstyle> </mml:math> scales like <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:msup> <mml:mi>N</mml:mi> <mml:mi>ν</mml:mi> </mml:msup> </mml:mstyle> </mml:math> where the scaling exponent ν takes different values on either side of the phase transition. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>β</mml:mi> <mml:mo>></mml:mo> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mstyle> </mml:math> we find that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mstyle> </mml:math> which is consistent with our analytic predictions for a non-continuum phase in the large β regime. For <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>β</mml:mi> <mml:mo><</mml:mo> <mml:msub> <mml:mi>β</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mstyle> </mml:math> we find that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:mstyle> </mml:math> , 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi mathvariant="normal">d</mml:mi> </mml:mrow> </mml:mstyle> </mml:math> causal set quantum gravity for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mstyle displaystyle="false"> <mml:mi>N</mml:mi> <mml:mo>≳</mml:mo> <mml:mn>65</mml:mn> </mml:mstyle> </mml:math> .
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".