Topological Phase Transitions and Their Thermodynamic Fate in Arbitrary- S Classical Pyrochlore Spin Ice

This research classifies topological phases and critical behavior in classical spin-$S$ pyrochlore magnets using thermodynamic energy convexity and Renormalization Group analysis. It systematically maps system behavior based on spin value $S$, revealing a dichotomy between continuous transitions ($S=1, S eq 3/2$) and a protected first-order transition at $S=3/2$.

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