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 PoissonDirichlet 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.

Automated summary

We quantitatively characterize weakly first-order thermal phase transitions in three-dimensional spin-one quantum magnets out of planar spin-nematic states using Poisson-Dirichlet distributions (PDs) and large-scale quantum Monte Carlo calculations. The thermal melting of the nematic state is identified to be a weakly first-order transition based on thermal properties and the distribution of the nematic order parameter, contrary to previous claims. Exact results for the order parameter distribution and Binder cumulants at the discontinuous melting transition are obtained through PD calculations. 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.