Poisson-Dirichlet distributions and weakly first-order spin-nematic phase transitions

We provide a quantitative characterization of generic weakly first-order thermal phase transitions out of planar spin-nematic states in three-dimensional spin-one quantum magnets, based on calculations using Poisson-Dirichlet distributions (PDs) within a universal loop model formulation, combined with large-scale quantum Monte Carlo calculations. In contrast to earlier claims, the thermal melting of the nematic state is not continuous, instead a weakly first-order transition is identified from both thermal properties and the distribution of the nematic order parameter. Furthermore, based on PD calculations, we obtain exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition. Our findings establish the thermal melting of planar spin-nematic states as a generic platform for quantitative approaches to weakly first-order phase transitions in quantum systems with a continuous SU(2) internal symmetry.

Figure 1

Illustration of the loop model on different small lattices (for $H$, $\mathrm{\Lambda }$ is the cubic lattice).

Figure 2

Comparison of the nematic histogram obtained from QMC at $u=cot(3\pi /8)$ with the PD prediction for $\eta =0.9021\left(2\right)$. The inset shows the histogram for various $L$ at the transition temperature $T_c=1.64900\left(1\right)$.

Figure 3

Temperature dependence of the Binder cumulant $U_Q$ near the phase transition for different system sizes at $u=cot(3\pi /8)$ from QMC. The PD-based predictions $U_Q^{-}$ in the ordered phase and $U_Q^c$ at the transition temperature $T_c$ are indicated by dashed lines. The right inset shows the $u$ dependence of the second moment ${\langle Q^2\rangle }_{\beta }$.

Figure 4

Temperature dependence of the specific heat $C$ for different system sizes at $u=cot(3\pi /8)$ from QMC. The inset shows the scaling of the maximum $C^{\text{max}}$ with system size, extracted from the shown Lorentzian interpolations.