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We attribute this difference to the improved frequency treatment and numerical integration scheme employed in the present pf-FRG implementation, which enable a more reliable resolution of low-energy instabilities at scales \u039b\u22720.02J compared to Ref.\u00a0[39]. In addition, we employ a more stringent criterion for identifying the flow breakdown. Further details are discussed in the End Matter.","type":"other"},{"key":"87fn-g2j3Cc47R1","unstructured":"It is worth noting that, for the classical model on the regular pyrochlore lattice with only nearest-neighbor interactions, all magnetically ordered phases identified to date correspond to commensurate q=0 magnetic orders [15, 16, 17].","type":"other"},{"key":"87fn-g2j3Cc48R1","unstructured":"A. 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All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"American Physical Society","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"066504"}}