{"paper":{"title":"Unveiling the nature of three dimensional orbital ordering transitions: the case of $e_g$ and $t_{2g}$ models on the cubic lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.str-el","authors_text":"Andreas M. L\\\"auchli, Sandro Wenzel","submitted_at":"2011-01-17T16:35:04Z","abstract_excerpt":"We perform large scale finite-temperature Monte Carlo simulations of the classical $e_g$ and $t_{2g}$ orbital models on the simple cubic lattice in three dimensions. The $e_g$ model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent $\\nu\\approx0.66(1)$ is close to the 3D XY value, the exponent $\\eta \\approx 0.15(1)$ differs substantially from O(N) values. At $T_c$ a U(1) symmetry emerges, which persists for $T<T_c$ below a crossover length scaling as $\\Lambda \\sim \\xi^a$, with an unusually small $a\\approx1.3$. Finally, for the $t_{2g}$ m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3259","kind":"arxiv","version":2},"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"}