{"paper":{"title":"Generalized Random Energy Model at Complex Temperatures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math-ph","math.CV","math.MP"],"primary_cat":"math.PR","authors_text":"Anton Klimovsky, Zakhar Kabluchko","submitted_at":"2014-02-10T13:44:25Z","abstract_excerpt":"Motivated by the Lee--Yang approach to phase transitions, we study the partition function of the Generalized Random Energy Model (GREM) at complex inverse temperature $\\beta$. We compute the limiting log-partition function and describe the fluctuations of the partition function. For the GREM with $d$ levels, in total, there are $\\frac 12 (d+1)(d+2)$ phases, each of which can symbolically be encoded as $G^{d_1}F^{d_2}E^{d_3}$ with $d_1,d_2,d_3\\in\\mathbb{N}_0$ such that $d_1+d_2+d_3=d$. In phase $G^{d_1}F^{d_2}E^{d_3}$, the first $d_1$ levels (counting from the root of the GREM tree) are in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2142","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"}