Spin glasses are frustrating. Although the ideas have been around for decades and form the foundation of countless complex systems models, they have nonetheless resisted researchers' efforts to understand exactly how they work – something three SFI scientists hope to change starting with a five-day working group at SFI in July.

Spin models were originally introduced to study materials made up of tiny magnets with varying orientations – so-called spins – at the atomic scale. In a household fridge magnet, the "spins" prefer to be aligned, and that overall preference results in a magnetization useful for suspending a child's report card or grocery list.

But the picture is not always so simple: In spin glasses each spin prefers to align with some of its neighbors, while being anti-aligned with others. These conflicting interactions can leave a spin in a quandary: which neighbors should it agree with?

This frustration – that is the technical term – and researchers' frustration when trying to understand spin glass dynamics is not limited to magnets, says SFI Omidyar Fellow Ruben Andrist, who along with SFI External Professors Jon Machta and Helmut Katzgraber is organizing the working group.

"It is not just a [problem in a] single field," Andrist says, citing examples in fields from quantum computing to voting models, where "frustrated spins" represent voters trying to decide between political parties. While there is inherent interest in solving such models, their complexity makes solving them very challenging, he says.

The working group will lead off with a basic question, he says: "Can we even make a statement about how computationally complex a problem typically is?" In the worst case, spin glass problems are among the hardest to solve, he says, but the typical case could be easier, and figuring that out would already be a step forward.

The group will review several recent developments in the field and, they hope, develop measures of difficulty that will aid researchers' efforts to study spin glasses across disciplinary boundaries.

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Getting to the heart of frustrated magnetism

## Macksb

Winfree's law is a mathematical law. It has been confirmed by mathematicians (e.g., Strogatz and Stewart) and applied successfully to biology (e.g., by Winfree himself and Ermentrout), but physicists have ignored it.

In Santa Fe terms, Winfree's law describes a self-organizing system. It's also a quantum system. Periodic oscillators have a tendency to sync, and when they do, they sync in certain ways identified by Winfree, and no other ways. So periodic oscillators self-organize their oscillations and themselves according to Winfree's law; and the permissible patterns are quantum as conceived by Planck: use an identified pattern or no sync. Each pattern is a quantum.

## Macksb

Nature prefers Winfree patterns that use the simplest Winfree pattern and the lowest possible N. That brings us to the spin "quandary" mentioned in the article. Groups of similar spins will be of a size that is the smallest possible. The groups must be regular (same number of spins or slightly varied, systematically, if dictated by the constraints of the material). A higher level of primary Winfree self-organization in the substance may govern first. The final result will be a solution that is commensurate with these constraints. A bit fuzzy, yes, but that is the way Winfree's law works.