{"id":"openai-math/A-radial-continuum-phase-transition-with-algebraic-decay","pdf":"https://github.com/openai/math/blob/main/preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-radial-continuum-phase-transition-with-algebraic-decay-September-24-2026","tags":["statistical-mechanics","phase-transitions","pair-potentials"],"score":0,"title":"A radial continuum phase transition with algebraic decay","domain":"Probability and statistical mechanics","family":"228","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We construct a bounded, continuous, stable radial pair potential in three dimensions with $`|\\phi(r)|\\le Cr^{-3-1/32}`$ for r ≥ 1. Throughout an open interval of positive densities, its canonical thermodynamic free energy is finite at every positive inverse temperature and has a strict downward derivative jump at one common finite positive inverse temperature.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Continuum phase transitions for radial pair potentials"}