{"paper":{"title":"Anomalous free energy expansions of planar Coulomb gases: multi-component and conformal singularity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Sung-Soo Byun","submitted_at":"2025-08-01T04:56:36Z","abstract_excerpt":"We study the partition function $$ Z_n = \\int_{\\mathbb{C}^n } \\prod_{1 \\le j<k \\le n} |z_{j}-z_{k}|^{2} \\prod_{j=1}^{n} |z_j|^{2c}\\, e^{-n V(z_{j})}\\frac{d^{2}z_{j}}{\\pi}, $$ where $c>-1$ and $$ V(z)= |z|^{2d}-t(z^{d}+\\overline{z}^{d}), \\qquad t >0, \\, d \\in \\mathbb{N}. $$ The associated droplet reveals a topological phase transition: for $t > 1/\\sqrt{d}$, it consists of $d$ connected components; whereas for $t < 1/\\sqrt{d}$, it becomes simply connected and contains the origin, where a conformal singularity arises. In both regimes, we establish the asymptotic expansion $$ \\log Z_n = C_1 n^2 + "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.00316","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.00316/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}