Does LiHo_xY_1-xF4 have a true spin-glass phase and quantum transition?
In plain words
LiHoYF4 is a crystal in which magnetic holmium ions are diluted by nonmagnetic yttrium, and a sideways field adds quantum fluctuations. Experiments disagree on whether its low-temperature state is a genuine spin glass, so it is unclear whether it realizes a quantum spin-glass transition.
Precise statement
In LiHo_xY_1-xF4 with x of about 0.17 to 0.2 (dipolar Ising moments along c, transverse field $H_t$ perpendicular to c), determine whether the nonlinear susceptibility diverges at a finite $T_g(H_t)$ and whether $T_g(H_t)$ ends at a $T = 0$ quantum critical point, given the random longitudinal fields generated by $H_t$ and the hyperfine coupling to Ho nuclei. An answer is a measured phase boundary with critical exponents, or evidence that no thermodynamic glass transition exists.
What would settle it
Equilibrium nonlinear ac susceptibility and noise measurements below 0.1 K on samples of controlled x, analyzed by critical scaling and compared with Monte Carlo of the dipolar model including hyperfine terms.
Status in the literature
Jonsson et al. (PRL 2007) reported no glass transition at $x = 0.167$ while Ancona-Torres et al. (PRL 2008) reported one; field-induced random fields complicate the transverse-field phase diagram.