Is QEG's asymptotic safe point an example of self criticality?by MTd2 Tags: asymptotic, criticality, point, safe 

#1
Mar612, 01:03 PM

P: 1,927

According to wikipedia:
"In physics, selforganized 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 scaleinvariance 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/Selforganized_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/hepth/0412307 Selforganized 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 spacetime from a discrete microscopic dynamics may be a selforganized 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? 



#2
Mar612, 03:18 PM

Sci Advisor
P: 8,007

All the fixed points are scale invariant. However, in general the require tuning, so they wouldn't be "selforganized".
Gauge/gravity examples in which the gauge theory is a CFT are examples of a gauge theory at a fixed point. 



#3
Mar612, 03:20 PM

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Where can you show me the fine tuning?




#4
Mar612, 03:23 PM

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



#5
Mar612, 03:41 PM

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Won't they naturally converge to that surface?




#6
Mar612, 04:24 PM

Sci Advisor
P: 8,007

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." 



#7
Mar612, 11:11 PM

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But the definition from wikipedia talks about an atractor. That doesn't mean it should reach there.




#8
Mar612, 11:21 PM

Sci Advisor
P: 8,007

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. 



#9
Mar1412, 11:15 PM

P: 1,927




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