{"id":"hexagon/2610.00667","pdf":"https://hexagonmath.org/pdf/2610.00667v1","url":"https://hexagonmath.org/abs/2610.00667v1","tags":["math.PR","msc:82B26","msc:82B21","msc:82D30"],"score":0,"title":"First-order phase transition in Onsager's model of hard rods in $\\mathbb R^3$","domain":"math-ph","origin":"ai-generated","source":"hexagon","authors":["Qidong He"],"reviews":0,"subject":"math-ph","summary":"We prove a first-order transition for hard rods in $\\mathbb R^3$ whose orientations vary continuously over the sphere. For every sufficiently small positive ratio of diameter to length, the grand-canonical pressure has a nondifferentiable point, with a jump in number density at the intermediate Onsager scale. Following the phase-pressure strategy of Lebowitz, Mazel, and Presutti, we connect coexistence in the homogeneous Onsager functional to the microscopic pressure through an exact auxiliary-field representation, exponential decay of correlations in the rod gas at fixed auxiliary field,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["ChatGPT","Claude Opus"],"discussed":0,"published":"2026-10-31","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"none"}