Conrady's animation visualizes chaos cooling and 2D space crystalizing out

[marcus]

MTd2 spotted this interesting paper by Florian Conrady (Perimeter postdoc).

http://arxiv.org/abs/1009.3195
Space as a low-temperature regime of graphs
...
Florian Conrady (Perimeter Inst. Theor. Phys.)
...
... Simulations show that there is a transition between a low-temperature regime in which the graphs form triangulations of 2-dimensional surfaces and a high-temperature regime, where the surfaces disappear...

To go with this paper the author has provided two animations to watch:
http://www.florianconrady.com/simulations.html

The second one of these two simulations ("Model with 2D interactions") shows the crystalization of a 2D space out of chaos as it cools. There is a helpful description of the simulation there that one can read. Because the actual simulation needed to run for a long time before 2D space actually emerged, what is shown is only the initial 2 minutes of action. Then what has resulted by that time is rotated for inspection, so one can examine. Then there is a pause in the animation while time is speeded up, and the final end result is reached. This final result of the cooling/crystalization is then displayed and rotated for examination.

As I understand it, the process is purely combinatorial and only looks like it is occurring in 3D space because of the presentation software being used. The software is useful since it is easier to visualize the process of links joining when we can see it spatially as "approaching coming together", but there is no surrounding space and so no motion involved in the actual calculation. The only "space" here is what eventually emerges when the links finally get themselves properly connected in a recognizable 2D network.

The "atoms" of the process are single isolated links. At high temperature they appear as a kind of "gas". Like a cloud of random disconnected match-sticks, or toothpicks. Their eventual connections with each other are governed by a Hamiltonian which Conrady has devised.

 

[MTd2]

Time to be ignored again, but here it goes:

Compare the heat capacity x Temperature of a superconductor

http://en.wikipedia.org/wiki/File:Cvandrhovst.png

with figure 6 of the paper.

And the susceptibility vs. temperature:

(central plot)

http://uhp.iphy.ac.cn/images/zxdt_LaCu3Fe4O12.jpg

and Figure 8 of the paper.

Florian Conrady doesn't say anything about superconductivity on his paper. Weird.

 

[marcus]

MTd2, I'm not sure how far one can go based only on this simulation work by Conrady.
There are other papers by him that are more serious and mainstream, some co-authored with Freidel. You probably know them.

As I see it this paper is very different---more tentative and playful. It is an intriguing idea that space would assemble itself as it "cooled".

But look at the artificially contrived Hamiltonian. This is how one starts out but it is not yet the real thing IMHO. It looks to me like he just arrived at the Hamiltonian by trial-and-error improvisation---as a device to make happen what he wants to happen.

It is, however, quite simple---which is nice.

I don't think the Hamiltonian is in any way "natural". And I don't know what else it could do besides cause 2D surfaces to assemble themselves out of hot fragmented chaos. I wonder if one could extend this trick to 3D. How would it be done?

My feeling is maybe the most interesting thing is the USE MADE OF UBIGRAPH computer tool. It demonstrates how to use Ubigraph to visualize the dynamic behavior of graphs. So suppose one found a way to do something more: introduce matter, make the graph do something more than just crystallize and rotate itself for inspection. Whatever else one could think of to make a graph do, Conrady shows us that we can turn the resulting combinatorial process (just a data structure, a bunch of lists) into an animated visual--a movie.

http://ubietylab.net/ubigraph/