{"id":"openai-math/A-continuum-temperature-singularity-for-a-radial-pair-potential","pdf":"https://github.com/openai/math/blob/main/preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-continuum-temperature-singularity-for-a-radial-pair-potential-September-24-2026","tags":["statistical-mechanics","pair-potentials","phase-transitions","free-energy"],"score":0,"title":"A continuum temperature singularity for a radial pair potential","domain":"Probability and statistical mechanics","family":"228","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.PR","summary":"We construct a stable radial pair potential in three dimensions whose canonical free energy has a strict downward derivative jump at one common finite positive inverse temperature throughout an open interval of positive densities. The potential has a divergent repulsive core, a nontrivial attractive interval, and an integrable tail satisfying $`\\phi(r)=o(r^{-3})`$. Its free-cube canonical free energy is finite at every positive inverse temperature and density.","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"}