Universality class of the Mott critical endpoint in organic conductors
In plain words
Squeezing certain organic salts turns them from Mott insulators into metals through a jump, like liquid turning into gas, that ends at a critical point; the measured critical exponents disagree with the liquid-gas prediction.
Precise statement
In kappa-(BEDT-TTF)2Cu[N(CN)2]Cl the first-order Mott metal-insulator line ends at a critical point near $T_{\mathrm{cr}} \sim 40\ \mathrm{K}$ and $P_{\mathrm{cr}} \sim 250\ \mathrm{bar}$. Conductivity scaling (Kagawa, Miyagawa, Kanoda, Nature 2005) gave $\beta \sim 1$ and $\delta \sim 2$, far from 3D Ising values ($\beta \sim 0.33,\ \delta \sim 4.8$) and from 2D Ising ($\beta = 1/8,\ \delta = 15$). Determine the universality class of the endpoint and how conductivity couples to the scaling fields (order parameter and energy density). An answer is a set of thermodynamic exponents (thermal expansion, compressibility, specific heat) measured at the endpoint, plus a theory of conductivity scaling consistent with them.
What would settle it
Thermodynamic critical exponents measured near $T_{\mathrm{cr}}$ with pressure resolution sufficient to separate Ising classes, together with a model that maps the scaling fields onto the measured conductivity exponents.
Status in the literature
Furukawa et al. (Nature Physics 2015) reported quantum-critical scaling of resistivity across the high-temperature Mott crossover; the class of the finite-temperature endpoint is still unsettled.