Magnetic order survives weak quantum fluctuations in gapless magnets

A recent study published in Physical Review Letters reveals that magnetic order can persist in gapless magnets despite weak quantum fluctuations. The researchers demonstrated robust ferromagnetism within the two-dimensional random-bond quantum Ising model, confirming a long-standing conjecture in quantum statistical mechanics. Magnetic order typically arises from spontaneous symmetry breaking, which physicists have long sought to prove is stable against perturbations like quantum fluctuations.

However, existing proofs often require the system to possess an energy gap, which disordered magnets such as the random-bond Ising model lack. To address this, the researchers developed a proof technique that doesn't rely on an energy gap, adapting the Peierls argument from statistical mechanics to quantum systems. The Ising model, a simplified description of a magnet, consists of spins on a lattice that interact with their nearest neighbors.

In classical physics, spins prefer to align due to interactions, leading to spontaneous symmetry breaking. In quantum mechanics, the ground state is a superposition of all spins aligning up or down. The researchers introduced a weak quantum perturbation, such as a transverse magnetic field, and required the Peierls condition to hold for domain walls that span the entire system.

They showed that low-energy states, like the ground state, cannot afford such domain walls, proving that the magnet remains ordered even in the presence of weak quantum fluctuations.