A pendulum swings not in a single plane but in five dimensions at once. Its motion is described by a complex mathematical model, and the pendulum itself is an electron in a graphene sheet interacting with five different "flavors" of its environment. Until now, simulating such a pendulum on a computer was painfully slow: each step required checking a huge number of possibilities.

A team of physicists led by Ashish Vaswani developed an optimized quantum Monte Carlo method (a calculation using random numbers). They "placed" the electron on the lowest Landau level, like forcing the pendulum to swing with only one allowed amplitude, discarding extra motions. This trick allowed them to simulate systems of up to 140 magnetic cells on the surface of a donut (torus) and up to 49 on a sphere — record-breaking sizes.

The most interesting part came when the scientists began to vary the interaction strength. At weak coupling, the five "swings" of the pendulum moved in sync — an ordered phase. At strong coupling, the sync broke down and the system became chaotic. Between them, they found a critical point, like the boundary between day and night, where properties change abruptly. And if you slightly break the symmetry between dimensions, the point becomes multicritical, reminiscent of a phase transition in quantum magnets between antiferromagnetic order (alternating spins) and a valence-bond state.

It is not yet clear what this liquid looks like in an infinitely large system: it resembles neither an ordinary insulator nor conformal field theory (a description of critical phenomena). But the found multicritical point answers a long-standing question about the global structure of the model's phase diagram. And the new computational framework opens the door to systematic studies of other systems — from flat bands in correlated materials to the fractional quantum Hall effect. So the pendulum, starting with five dimensions, led physicists to a universal tool for exploring the quantum world.