Is QEG's asymptotic safe point an example of self criticality?

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Discussion Overview

The discussion revolves around the relationship between asymptotic safety (AS) in quantum gravity and the concept of self-organized criticality (SOC). Participants explore whether the asymptotic safe point can be considered an example of SOC, examining definitions and implications within the context of quantum gravity and spin networks.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • Some participants reference the definition of self-organized criticality from Wikipedia, suggesting that the asymptotic safe point aligns with this description.
  • Others argue that while fixed points are scale invariant, they generally require tuning, which contradicts the notion of being "self-organized."
  • A participant questions the existence of fine-tuning in the context of asymptotic safety, prompting further discussion on the parameters needed to remain on the critical surface.
  • Another participant asserts that not all trajectories converge to the asymptotic safe surface, indicating that some may not exhibit asymptotic safety despite proximity to the fixed point.
  • Concerns are raised about the implications of the Wikipedia definition regarding attractors and whether systems need to reach the fixed point to be considered self-organized.
  • There is uncertainty expressed about the existence of self-organized criticality itself, with participants sharing links to external resources for further exploration.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the asymptotic safe point exemplifies self-organized criticality. Multiple competing views remain regarding the definitions and implications of both concepts.

Contextual Notes

Participants highlight the dependence on definitions of self-organized criticality and asymptotic safety, as well as the unresolved nature of fine-tuning parameters and trajectories in relation to fixed points.

MTd2
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According to wikipedia:

"In physics, self-organized criticality (SOC) is a property of (classes of) dynamical systems which have a critical point as an attractor. Their macroscopic behaviour thus displays the spatial and/or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to precise values."

http://en.wikipedia.org/wiki/Self-organized_criticality

The asymptotic safe point pretty much fits this description, apparently.

In relation to Quantum Gravity, the only thing I could find was this:

http://arxiv.org/abs/hep-th/0412307

Self-organized criticality in quantum gravity

Mohammad H. Ansari, Lee Smolin
(Submitted on 27 Dec 2004 (v1), last revised 18 May 2005 (this version, v5))
We study a simple model of spin network evolution motivated by the hypothesis that the emergence of classical space-time from a discrete microscopic dynamics may be a self-organized critical process. Self organized critical systems are statistical systems that naturally evolve without fine tuning to critical states in which correlation functions are scale invariant. We study several rules for evolution of frozen spin networks in which the spins labelling the edges evolve on a fixed graph. We find evidence for a set of rules which behaves analogously to sand pile models in which a critical state emerges without fine tuning, in which some correlation functions become scale invariant.

****

Perhaps this is a clue that AS is really related to spin networks?
 
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All the fixed points are scale invariant. However, in general the require tuning, so they wouldn't be "self-organized".

Gauge/gravity examples in which the gauge theory is a CFT are examples of a gauge theory at a fixed point.
 
Where can you show me the fine tuning?
 
MTd2 said:
Where can you show me the fine tuning?

In AS, the fine tuning are the parameters to stay on the critical surface in which the fixed point lies.
 
Won't they naturally converge to that surface?
 
No. There are trajectories that are not asymptotically safe. But such trajectories may pass near enough to the fixed point that the fixed point properties affect the low energy theory.

http://arxiv.org/abs/1008.3621
"Now let us consider statement (2) from the point of view of “emergence”, i.e. for a trajectory that is close to asymptotic safety but not exactly safe. The closer such trajectory gets to the FP, the longer the time it passes there."
 
But the definition from wikipedia talks about an atractor. That doesn't mean it should reach there.
 
Does SOC exist?

Anyway, if it's off the critical surface, it will eventually go away from the fixed point.

But AS could be related to LQG anyway, since many believe LQG needs some sort of fixed point.
 
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