Origin of universal H/T scaling in disordered frustrated magnets
In plain words
In several frustrated magnets with chemical disorder, heat capacity and magnetization measured at many fields and temperatures fall onto one curve when plotted against field divided by temperature. The collapse points to a common population of weakly bound spin pairs, but no microscopic theory has yet predicted the exponent for a specific material.
Precise statement
In H3LiIr2O6 and several other disordered frustrated magnets the data obey $C/T \sim T^{-\gamma} F_C(\mu_B H/k_B T)$ and $M \sim H^{(1-\gamma)} F_M(\mu_B H/k_B T)$ with a material-dependent $\gamma$ between 0 and 1 (Kimchi, Sheckelton, McQueen, Lee, Nature Communications 2018), attributed to a power-law distribution of singlet energies $P(J) \sim J^{-\gamma}$. Derive $\gamma$ and the scaling functions $F_C, F_M$ from a microscopic disordered model of at least one compound, and determine whether $\gamma$ is fixed by a 2D random-singlet fixed point or is nonuniversal. An answer is a model whose computed $\gamma$ and $F_C$ agree with the data without fitting $\gamma$.
What would settle it
Strong-disorder renormalization or quantum Monte Carlo of a calibrated random-exchange model that reproduces the measured $\gamma$ and scaling functions of one compound.