The Bose glass consists of interacting and disordered, or “dirty,” bosons—a system that describes helium-$4$ in porous media, cold atoms in disordered optical potentials, disordered magnetic insulators, and thin superconducting films. At zero temperature, and as the degree of disorder is reduced, the Bose glass undergoes a phase transition to a superfluid, but experiments and numerical simulations disagree with the scaling laws of the phase change predicted by theory. Writing in *Physical Review Letters*, Zhiyuan Yao at the University of Massachusetts, Amherst, and co-workers present new simulations that resolve this discrepancy.

A tenet of statistical physics is the notion of universality: Seemingly dissimilar physical systems—like the orientation of spins in a magnet and the position of atoms in a metal alloy—behave in a “universal” fashion near a continuous phase transition. Near a critical point, the critical temperature ${T}_{c}$ follows the scaling relation ${T}_{c}\propto ({g}_{c}-g{)}^{\varphi}$, where $g$ is a control parameter (such as a magnetic field or the amount of disorder) that drives the phase transition. Any physical system in the universality class of the Bose glass-superfluid phase transition will have the same value for the critical exponent $\varphi $.

Recent measurements and simulations of the Bose glass to superfluid phase transition found a critical exponent $\varphi $ that disagreed with the expected scaling behavior based on this system’s universality class. To resolve this ‟$\varphi $ crisis,” Yao and his colleagues performed quantum Monte Carlo simulations on lattices at least ten times larger than previous works. They also adopted a new strategy of using the amount of disorder in the lattice of bosons, instead of the chemical potential, as the control parameter. The team arrived at a precise value of the critical exponent $\varphi =2.7(2)$—the value expected for this system’s universality class—and showed that previous studies likely underestimated $\varphi $ because they were performed too far from the quantum critical region to observe the true scaling behavior. – *Kevin Dusling*