Is the 2D random-singlet state one phase with finite dynamic exponent?
In plain words
In one dimension, random couplings produce the random-singlet state, where spins pair at all distances and time scales grow exponentially with length. Simulations in two dimensions find a similar pairing state with time scales growing only as a power of length, and whether it is one universal phase is unclear.
Precise statement
For 2D $S = 1/2$ models with random couplings (random $J-Q$ model on the square lattice; random-bond frustrated Heisenberg models on square, triangular and kagome lattices), determine whether the disordered nonmagnetic state is a single phase controlled by one fixed point, the value of its dynamic exponent $z$ (finite, or infinite as in 1D), and the exponent of the algebraic decay of the mean spin correlation. An answer gives $z$ and the correlation exponent with error bars for each model, or shows that they vary continuously.
What would settle it
Sign-problem-free quantum Monte Carlo of random $J-Q$ models on lattices with $L \ge 128$, together with DMRG or tensor-network studies of frustrated random-bond models, compared on the same observables.
Status in the literature
Liu, Shao, Lin, Guo and Sandvik (PRX 2018) found a 2D random-singlet state in the random J-Q model with a finite dynamic exponent that varies across the phase diagram; frustrated random models have not been tested at comparable sizes.