{"paper":{"title":"Mermin-Wagner at the Crossover Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-lat"],"primary_cat":"cond-mat.str-el","authors_text":"Christoph P. Hofmann","submitted_at":"2017-11-27T21:11:49Z","abstract_excerpt":"Mermin-Wagner excludes spontaneous (staggered) magnetization in isotropic ferromagnetic (antiferromagnetic) Heisenberg models at finite temperature in spatial dimensions $d \\le 2$. While the proof relies on the Bogoliubov inequality, here we illuminate the theorem from an effective field theory point of view. We estimate the crossover temperature $T_c$ and show that, in weak external fields $H$, it tends to zero: $T_c \\propto \\sqrt{H}$ ($d=1$) and $T_c \\propto 1/|\\ln H|$ ($d=2$). Including the case $d$=3, we derive upper bounds for the (staggered) magnetization by combining microscopic and eff"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.10003","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}