Physicists Prove Magnetic Order Survives Quantum Fluctuations in Gapless, Disordered Magnets

A magnet is a system in which billions of tiny spins agree to point the same way. Heat scrambles that agreement. So, in principle, does quantum mechanics, which lets spins fluctuate even at absolute zero. A new proof from physicists at the University of Colorado Boulder shows that, in a broad and messy class of magnets, weak quantum fluctuations are not enough to destroy the order.

The work, by Chao Yin and Andrew Lucas, was published in Physical Review Letters in 2026 (DOI 10.1103/5ntb-ggcz). It establishes robust ferromagnetism in the two-dimensional random-bond quantum Ising model, confirming a longstanding conjecture in quantum statistical mechanics. In that model, the strength of the coupling between neighboring spins varies randomly from bond to bond, which is a stand-in for real, imperfect materials.

The difficulty was a technical one. Existing proofs that quantum order survives typically rely on the system having an energy gap, a minimum cost to excite it above its lowest-energy state. Disordered magnets such as the random-bond Ising model are gapless, so those proofs could not reach them.

Yin and Lucas instead adapted the Peierls argument, a classical method from statistical mechanics. The classical version asks what it costs for a region of flipped spins to form inside an ordered magnet. The team formulated a quantum Peierls condition: low-energy states cannot contain domain walls that span the whole system. They added weak quantum perturbations, such as a transverse magnetic field, to a classical Ising model and tracked how clusters of flipped spins affect the magnetism.

Their central insight is about cost. "Each step costs energy," Lucas explained. "The chance of finding a complete wall therefore shrinks exponentially with its length." Small clusters can flip cheaply, but a wall long enough to cut the magnet in two is prohibitively expensive, so global order persists.

For experimentalists, the result offers reassurance rather than a new device. Real magnets always contain some disorder, from missing atoms to uneven bonds, and the proof says that in this class of model a modest amount of quantum jitter does not wipe out the ordered state. That helps theorists decide where to look when they ask which disordered quantum materials can hold a stable phase at all.

The result is a step toward a longer-term goal in condensed-matter theory, classifying gapless quantum phases of matter, which are far less understood than gapped ones. It has limits. The method does not yet handle mobile excitations such as sound waves or photons, which can behave differently from the localized spin clusters the proof treats. Even so, it replaces a decades-old conjecture with a rigorous result and gives theorists a new tool that does not depend on an energy gap.