The science behind the Network Game

The Network game is a gamification of the Sherrington-Kirkpatrick model (SK). This is a toy model for a spin-glass with infinite range interactions. Spin-glass are of great fundamental interest since they describe a fundamentally different state of matter.

Spin-glass describes a magnet with disorder. Let’s take that piece by piece. A magnet consists of spins, which describes the magnetic orientation of each atom. In the SK model, this orientation can be positive or negative, which is typically represented by an arrow. The negative and positive orientation corresponds to the sphere and cube in the game. Hence, you're really flipping magnetic spins when you're playing the game.

The typical fridge magnet you have at home is a so-called ferromagnet. This magnet can stick to metal since almost all spins point in the same direction, which makes this system very ordered. However, in a spin-glass, most of the spins point in different directions with seemly no large scale pattern. This is what is known as disorder. This effect arises due to the many cyan and white connections that favor spins pointing in different or identical directions.

This type of disorder is also found in other physical systems such as glass. In glass, the atoms are placed in an disorder structure. This analogy is what gives the name spin-glass. This is a very different type of structure from the regular crystalline structure found in metals.
It is very difficult to find the best configuration for a given set of connections. If we check some configuration of spins, it is difficult to rule out that a better configuration exists. The only way to ensure this, is to simply check all possible configurations. Clearly, you wouldn’t do this yourself, but get some supercomputer to do it. However, the time needed to perform such a calculation is simply … beyond comprehension. It could easily take thousands of years or the entire lifetime of the universe. This is simply a roadblock towards a better understanding of spin-glasses.
This type of extremely difficult computational problems are known as NP-hard problems. The approach here is not to simply build a faster computer, but to design better algorithms that find good enough solutions. So, how can we find such solutions? Humans are good at creative guesswork, and in this game, we want to see if you can help us find good solutions.