{"paper":{"title":"On the thermodynamics of the black hole and hairy black hole transitions in the asymptotically flat spacetime with a box","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Bin Wang, Yan Peng, Yunqi Liu","submitted_at":"2017-08-04T08:10:26Z","abstract_excerpt":"We study the asymptotically flat quasi-local black hole/hairy black hole model with nonzero mass of the scalar filed. We disclose effects of the scalar mass on transitions in a grand canonical ensemble with condensation behaviors of a parameter $\\psi_{2}$, which is similar to approaches in holographic theories. We find that more negative scalar mass makes the phase transition easier to happen. We also obtain an analytical relation $\\psi_{2}\\varpropto(T_{c}-T)^{1/2}$ around the critical phase transition points implying a second order phase transition. Besides the parameter $\\psi_{2}$, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01411","kind":"arxiv","version":3},"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"}