This article has been reviewed according to Science X's editorial process and policies. Editors have highlighted the following attributes while ensuring the content's credibility: In a new study published in Physical Review Letters, researchers have shown that magnetic order can survive weak quantum fluctuations in disordered magnets that lack an energy gap. The work establishes robust ferromagnetism in the two-dimensional random-bond quantum Ising model, confirming a longstanding conjecture in quantum statistical mechanics.
Many magnets owe their order to spontaneous symmetry breaking (SSB). Physicists have long sought to prove that this order is stable against perturbations such as quantum fluctuations. Existing proofs, however, typically require the system to have an energy gap.
Disordered magnets such as the random-bond Ising model are gapless, placing them outside the reach of these proofs. The researchers developed a proof technique that does not rely on an energy gap. They adapted an argument from statistical mechanics, known as the Peierls argument, to quantum systems.
Phys.org spoke to co-author Andrew Lucas of the University of Colorado Boulder about the work. "[Co-author] Chao and I have been interested in the stability of matter for multiple years now, ever since he was my Ph.D. student, so it was natural for us to think about problems in this space. More concretely, though, we simply happened to develop a very useful mathematical technique in 2024 that allows us to get very strong constraints on where many-body quantum states are supported.
This was a highly unusual idea, and it allowed us to look at the problem in the current paper from a fresh perspective," Lucas explained. The Ising model is a simplified description of a magnet. Each spin sits on a lattice, points either up or down, and interacts with its nearest neighbors.
"An individual spin does not care whether it is up or down; it only wants to align with its neighbor. The lowest-energy configurations have all spins pointing up, or all pointing down. Classically, the system would have to pick—this would spontaneously break a symmetry of the system (the energy doesn't change if we flip all spins together).
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