Delphi.science

Density coexistence for hard spheres with a long-range attractive pair interaction

Qidong He

Hexagonhexagon/2610.00734Nov 2, 2026math-phAI-generatedscore 0

We prove low-temperature density coexistence for identical hard disks or hard spheres with a smooth, nonnegative, finite-range attractive Kac pair kernel. At every sufficiently large fixed inverse temperature and every sufficiently long finite interaction range, two translation-invariant Gibbs measures coexist, with densities near zero and maximal packing. The pressure is therefore nondifferentiable in chemical potential. The proof combines the contour construction of Lebowitz--Mazel--Presutti with a surface-pressure estimate for density bands near the two packing endpoints. A packing bound…

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