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Researchers published a study in Physical Review Letters showing that magnetic order can survive weak quantum fluctuations in disordered magnets lacking an energy gap. This work confirms a longstanding conjecture regarding the stability of ferromagnetism in two-dimensional random-bond quantum Ising models. Unlike previous proofs, this method does not require the system to have an energy gap, which is the minimum energy needed to excite a system above its ground state.

The study adapts the Peierls argument, originally used for classical magnets, to apply to quantum systems without gaps. In these models, spins interact randomly; while most favor alignment, some favor anti-alignment, creating clusters that can flip at almost no energy cost. This makes the magnet gapless, meaning it lacks a minimum energy threshold for excitation. The researchers proved that as long as random interactions are sufficiently biased toward alignment, the system remains ordered despite these fluctuations.

Co-author Andrew Lucas of the University of Colorado Boulder explained that their team developed a new mathematical technique in 2024 to constrain many-body quantum states. They formulated a quantum version of the Peierls condition, demonstrating that low-energy states cannot afford domain walls spanning the entire system. Although small clusters can flip easily, the probability of forming a complete wall shrinks exponentially with its length, ensuring magnetism persists.