Dualities and Topological Classification of the S=1 Pyrochlore Spin Ice

We derive dual descriptions of the trivial paramagnetic, Z 2-deconfined, and Z 2-confined U(1) Coulomb phases of the S=1 pyrochlore spin ice. In the monopole-free limit, the system can be effectively mapped onto 3D XY and Ising loop-gas models depending on the spin anisotropy, which provides theoretical estimates for the phase boundaries, while a macroscopic flux vector classifies the topological sectors via geometric parity rules. Thermal unit monopoles permit endpoints of both directed spin loops and unoriented vacancy loops. The resulting relevant symmetry-breaking fields in the dual XY and Ising descriptions predict rounded crossovers near the monopole-free critical points. Monte Carlo simulations support this monopole-induced rounding.