Is the 2D quantum spin-glass transition controlled by infinite randomness?
In plain words
In some disordered quantum magnets the transition is controlled by rare, strongly coupled regions, so time scales grow exponentially with length instead of as a power. In two dimensions simulations find that one kind of excitation behaves this way while another does not, and how the two fit into one critical theory is unsettled.
Precise statement
For the 2D transverse-field Edwards-Anderson model, H = -sum_<xy> J_xy sz_x sz_y - Gamma sum_x sx_x on the square lattice, the parity-even gap closes as L^-$z_e$ with finite z_e while the parity-odd gap Delta = E_0,odd - E_0,even has a fat-tailed distribution and closes faster than any power of $L$. Determine whether the odd gap obeys activated scaling $\ln(1/\Delta) \sim L^{\psi}$ with an ever-broadening distribution, as strong-disorder renormalization group predicts, and the value of $\psi$; and determine the scaling of the typical and average spin-glass susceptibility near Gamma_c, including any Griffiths divergence on the paramagnetic side. An answer gives $\psi$ (or excludes activated scaling) and the Griffiths exponents with error bars.
What would settle it
Strong-disorder renormalization group results checked against large-scale quantum Monte Carlo data for the full distributions of gaps and local susceptibilities at and near $\Gamma_{c}$.
Status in the literature
Unverified note
Bernaschi et al. (Nature 2024) found $z_{e} = 2.46(17)$ for parity-even excitations and a Levy-type fat-tailed parity-odd gap distribution; $\psi$ and the Griffiths behavior are not yet determined.