Monday, December 09, 2013

Spin Physics, Now in a Board Game

You've likely heard that "spin" is an important property in the world of quantum mechanics, but it's not quite the same as our everday sense of the word "spin." Instead, the spin of an elementary particle (such as a quark or electron) represents its intrinsic angular momentum, which isn't quite the same as the classical sense of angular momentum.

Spin can be tough to wrap your head around, but now there's an interactive way to appreciate what spin means: a board game. Physics professor Alexander K. Hartmann's (University of Oldenburg in Germary) board game, Spin Glasses, aims to bring spin to your living room.

In a style reminiscent of the popular game Othello, Spin Glasses pits two players against each other as they learn about the game's titular material (spin glasses): a complex and peculiar form of magnets. At first glance, the game looks fun yet challenging. And if you don't want to pay for the professional version, you can make your own game for free with a color printer, scissors, and glue.

A picture of Spin Glasses, a new board game focusing on quantum mechanics.
Image Credit: Alexander K. Hartmann


What Are Spin Glasses?


Spin glasses are a special breed of magnet that contain both ferromagnetic and anti-ferromagnetic bonds throughout. Consequently, scientists call them disordered magnets with "frustrated interactions." Both of these types of bonds connect the electrons of different atoms, but their differences lie in the types of electron spins that they connect.

For ferromagnetic bonds, same spins (e.g. two up-spins) are more energetically favorable. In anti-ferromagnetic bonds, on the other hand, opposite spins are more favorable.

So what makes them worth studying?

For one, structures containing these two conflicting sorts of bonds has a strong carryover to mathematical studies of complexity.

Take, for example, the Traveling Salesman Problem. The problem poses the following challenge: For a region with N cities, what's the shortest route for a salesman to take while visiting every city exactly once?

For a very small number of cities, the problem takes little effort to solve. Add just a few more cities, however, and the problem's difficulty increases substantially. Using a brute force method (checking every possible route and then selecting the shortest one) requires extremely large amounts of computing power for a relatively small number of cities.

Consequently, researchers must devise smarter algorithms to find optimal routes. In the world of spin glasses, researchers similarly try to find bond structures that produce the lowest energy state for the material — a task very similar to the one found in the Traveling Salesman Problem. In turn, this sort of complexity research can be applied to airline scheduling, pattern detection, and more.

Spin glasses have also generated interest from solid state physicists looking to explain phase transitions for liquids, solids, and glasses.

The magnetization for a Rubidium-87 Bose-Einstein Condensate. The colors indicate the direction of magnetization while brightness indicates the amplitude.
Image Credit: S.R. Leslie et. al/PRL/UC Berkeley

Game Time


In Hartmann's board game, two players compete to fill the board with the higher amount of "spin" circles (one player uses white spins and the other uses black), similar to the game Othello. Each turn, the players place either spin pieces or bond pieces (ferromagnetic or anti-ferromagnetic strips that connect two spin pieces) on the board.

Ferromagnetic bonds, which are represented by blue strips, prefer to connect two spins with the same color (e.g. two white circles). Anti-ferromagnetic bonds (red strips), however, require two connecting spins of opposite color. Consequently, depending on the order and placement of spins and bonds, players can force the opposing player's spins to flip over to their side. Remember: the point of the game is to finish with more spin pieces with your assigned color on the board than the other player.

Also, there's several "action cards" that allow players to bend the rules a bit. One card, for example, allows you to remove a bond from the table to your advantage. The game's rules have a few more quirks than I've outlined here, so you can read a more thorough description of the rules on Hartmann's arXiv paper (PDF).

Although I haven't played the game yet, there seems to be a relatively low barrier for entry considering the subject matter. Nonetheless, there's plenty of room for strategy in this game of spin reversal.

Here's an example of two turns from the game. The image on the left shows the board after the white player's turn. For her turn, the black player drew two ferromagnetic (blue) bonds and one spin piece. They chose to place the spin piece on the position marked "X," then they placed their two bond pieces. This forced the other two white pieces to flip over (blue bonds prefer spins with the same color). Thus, the image on the right shows the board after the black player's turn. Because of the order of the black player's moves during his turn, they were allowed to flip over the white pieces.
Image Credit: Alexander K. Hartmann

You can find full instructions and print out the necessary pieces to make your own game here (scroll to the last few pages).

Alternatively, you can email Hartmann's university (details in Hartmann's paper) to ship you a professional version of the game for 14.50 euros.

For another example of a quantum mechanics board game, check out Antimatter Matters. You can find our write-up of that game here.

No comments:

Post a Comment