If you squeeze an ordinary piece of metal, it heats up — even those who have pumped a bicycle tire know that. But what happens if you squeeze a magnet in which atomic arrows refuse to freeze even at absolute zero? A group of physicists decided to test this on special crystals — frustrated magnets, where the magnetic moments of atoms (tiny compasses) sit on a triangular lattice and cannot be friends with all neighbors at once.

They took two models: a simpler one with rigid up-down arrows (like in a toy compass), and a second where arrows can rotate freely but obey quantum laws. In both models, atoms sit at the nodes of a triangular lattice, like balls in a billiard triangle, except each ball is also a tiny magnet. Squeezing such a lattice changes the distances between atoms, and thus the strength of their magnetic interaction. The authors were interested in how entropy, a measure of the disorder reigning in the system, changes under compression.

The main tool was the Grüneisen parameter — a number that shows how strongly a material changes its size upon heating or cooling. In ordinary solids, this parameter is modest and predictable. But in triangular magnets, when compression brings the system to the point of maximum frustration (the very point where all neighbors are equally unhappy), the parameter skyrockets. It becomes huge at low temperatures, like a thermometer that goes off scale at the slightest touch. This is a universal sign that a huge reservoir of hidden disorder, residual entropy of the ground state, lurks in the material.

In the quantum version of the model with rotating arrows, the picture turned out to be more complex. At absolute zero, real rearrangements occur — phase transitions that change the magnetic pattern. And the Grüneisen parameter sensitively responds to each such rearrangement, acting as a detector of boundaries between different states. At moderate temperatures, however, the quantum model behaves almost classically — disorder reigns.

Thus, thermal expansion, a good old effect from a school textbook, turns into an ultrasensitive probe for the most entangled quantum states. Squeeze a crystal by a micron, and you know the mood of billions of atomic magnets.