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

Sena Watanabe; Yukitoshi Motome; Haruki Watanabe

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arXiv · 2603.03852

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

Sena Watanabe·Yukitoshi Motome·Haruki Watanabe

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Abstract

We resolve the phase diagram of the $S=1$ pyrochlore spin ice, which exhibits trivial paramagnetic, U(1) Coulomb, and spin nematic phases. 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. At finite temperatures, thermal monopoles act as a symmetry-breaking field in both 3D $XY$ and Ising loop-gas pictures, rounding the phase transitions into continuous crossovers. These theoretical findings are corroborated by classical Monte Carlo simulations.

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Sena Watanabe, Yukitoshi Motome, Haruki Watanabe. 2026-03-04. Dualities and Topological Classification of the $S=1$ Pyrochlore Spin Ice. https://arxiv.org/abs/2603.03852

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